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An ingeniously designed autoencoder (PrimeNet) using simulated observations of future generation ECHO satellite mission recovers CMB B mode map, angular spectrum for multipoles $\ell \lesssim 9$ and tensor to scalar ratio $r$ {\it limited only by cosmic variance down to $r= 0.0001$ and below}. We use diverse, realistically complex and detailed foreground models. PrimeNet predicts accurate results even when data with $r=0$ are tested which were not used in training, implying robust and efficient predictive power. The work eliminates a major bottleneck of weak CMB B mode reconstruction and takes a leap forward for understanding fundamental physics of the primordial Universe.

Policy Brief on "Regional and Global Collaborations in Astronomy", distilled from the corresponding panel that was part of the discussions during S20 Policy Webinar on Astroinformatics for Sustainable Development held on 6-7 July 2023. Astronomy brings together advanced scientific research, state-of-the-art technology, and educational initiatives, all while captivating and stimulating people of all ages. By doing so, it possesses the potential to serve as a powerful catalyst for sustainable global development and the resolution of global societal issues. It attracts a diverse range of scientists and experts from various fields, fostering collaboration and innovation. By leveraging their resources, influence, and diplomatic initiatives, S20 academies can foster an enabling environment for international collaborations in astronomy, facilitate knowledge exchange, and drive scientific advancements that benefit humanity. This policy brief explores the opportunities and challenges presented by regional and global collaborations in astronomy. The policy webinar took place during the G20 presidency in India (2023). A summary based on the seven panels can be found here: arxiv:2401.04623., Comment: 6 pages. The panel videos including keynotes and the white papers are available on the S20 site at: https://s20india.org/science-policy-webinar-astroinformatics-for-sustainable-development/

Policy Brief on "AstroInformatics, Recommendations for Global Collaboration", distilled from panel discussions during S20 Policy Webinar on Astroinformatics for Sustainable Development held on 6-7 July 2023. The deliberations encompassed a wide array of topics, including broad astroinformatics, sky surveys, large-scale international initiatives, global data repositories, space-related data, regional and international collaborative efforts, as well as workforce development within the field. These discussions comprehensively addressed the current status, notable achievements, and the manifold challenges that the field of astroinformatics currently confronts. The G20 nations present a unique opportunity due to their abundant human and technological capabilities, coupled with their widespread geographical representation. Leveraging these strengths, significant strides can be made in various domains. These include, but are not limited to, the advancement of STEM education and workforce development, the promotion of equitable resource utilization, and contributions to fields such as Earth Science and Climate Science. We present a concise overview, followed by specific recommendations that pertain to both ground-based and space data initiatives. Our team remains readily available to furnish further elaboration on any of these proposals as required. Furthermore, we anticipate further engagement during the upcoming G20 presidencies in Brazil (2024) and South Africa (2025) to ensure the continued discussion and realization of these objectives. The policy webinar took place during the G20 presidency in India (2023). Notes based on the seven panels will be separately published., Comment: 7 pages

We present a Bayesian inference method to characterise the dust emission properties using the well-known dust-HI correlation in the diffuse interstellar medium at Planck frequencies $\nu \ge 217$ GHz. We use the Galactic HI map from the Galactic All-Sky Survey (GASS) as a template to trace the Galactic dust emission. We jointly infer the pixel-dependent dust emissivity and the zero level present in the Planck intensity maps. We use the Hamiltonian Monte Carlo technique to sample the high dimensional parameter space ($D \sim 10^3$). We demonstrate that the methodology leads to unbiased recovery of dust emissivity per pixel and the zero level when applied to realistic Planck sky simulations over a 6300 deg$^2$ area around the Southern Galactic pole. As an application on data, we analyse the Planck intensity map at 353 GHz to jointly infer the pixel-dependent dust emissivity at Nside=32 resolution (1.8\deg\ pixel size) and the global offset. We find that the spatially varying dust emissivity has a mean of 0.031 MJysr$^{-1} (10^{20} \mathrm{cm^{-2}})^{-1}$ and $1\sigma$ standard deviation of 0.007 MJysr$^{-1} (10^{20} \mathrm{cm^{-2}})^{-1}$. The mean dust emissivity increases monotonically with increasing mean HI column density. We find that the inferred global offset is consistent with the expected level of Cosmic Infrared Background (CIB) monopole added to the Planck data at 353 GHz. This method is useful in studying the line-of-sight variations of dust spectral energy distribution in the multi-phase interstellar medium., Comment: 19 pages, 14 figures, Accepted for publication in MNRAS

The exquisitely measured maps of fluctuations in the Cosmic Microwave Background (CMB) present the possibility to test the principle of Statistical Isotropy (SI) of the Universe through systematic observable measures for non-Statistical Isotropy (nSI) features in the data. Recent measurements of the CMB temperature field provide tantalizing evidence of the deviation from SI. A systematic approach based on strong mathematical formulation allows any nSI feature to be traced to known physical effects or observational artefacts. Unexplained nSI features could have immense cosmological ramifications for the standard model of cosmology. BipoSH (Bipolar Spherical Harmonics) provides a general formalism for quantifying the departure from statistical isotropy for a field on a 2D sphere. We adopt a known reduction of the BipoSH functions, dubbed Minimal Harmonics (Manakov et al. 1996). We demonstrate that this reduction technique of BipoSH leads to a new generalized set of isotropic angular correlation functions (mBipoSH) that are observable quantifications of nSI features in a sky map. We show that any nSI feature in the CMB map captured by BipoSH at the bipolar multiple $L$ with projection $M$ can be studied by $(L+1)$ mBipoSH angular correlation functions in case of even parity and by $L$ functions in case of odd parity. We present in this letter a novel observable quantification of deviation from statistical isotropy in terms of generalized angular correlation functions that are compact and complementary to the BipoSH spectra that generalize angular power spectrum CMB fluctuations.

We address a current caveat in the deconvolution of the Primordial Power Spectrum (PPS), from observed Cosmic Microwave Background (CMB) temperature anisotropy, in the presence of weak lensing of the CMB by the large scale structure (LSS) in the Universe. Richardson-Lucy (RL) deconvolution algorithm has been used in the context of reconstructing a free-form PPS, $P_R(k)$ from the observed lensed CMB temperature anisotropy power spectrum $\widetilde{C}_{\ell}^{TT}$. We propose and demonstrate that the RL algorithm works in the context of a non-linear convolution where the non-linear contribution is small, such as the effect of weak lensing of the $\widetilde{C}_{\ell}^{TT}$, for the deconvolution of the PPS from it. The Non-Linear Iterative Richardson-Lucy (NIRL) algorithm is successful at both convergence, as well as fidelity, in reconstructing features in some underlying PPS. This makes PPS reconstruction efforts more robust in accounting for the weak lensing effect in the CMB temperature observations. No prior assumptions on the PPS are involved during the iterative delensing process, and distinct improvement is noted over a power-law template based delensing approach used earlier, at the cost of moderately increased computational cost due to the NIRL reconstruction kernel., Comment: 31 pages, 8 Figures (with subfigures), 10 Tables

Exploring Cosmic History and Origins (ECHO), popularly known as `CMB-Bh$\overline{a}$rat', is a space mission that has been proposed to the Indian Space Research Organisation (ISRO) for the scientific exploitation of the Cosmic Microwave Background (CMB) at the next level of precision and accuracy. The quest for the CMB polarization $B$-mode signals, generated by inflationary gravitational waves in the very early universe, is one of the key scientific goals of its experimental design. This work studies the potential of the proposed ECHO instrumental configuration to detect the target tensor-to-scalar ratio $r \sim 10^{-3}$ at $3\sigma$ significance level, which covers the predictions of a large class of inflationary models. We investigate the performance of two different component separation pipelines, NILC and Commander, for the measurement of $r$ in presence of different physically motivated models of astrophysical foregrounds. For a simplistic foreground model (only polarized dust and synchrotron), both component separation pipelines can achieve the desired sensitivity of ECHO, i.e. $\sigma (r =0) \sim (0.4 - 0.7)\times 10^{-3}$. NILC performs better than Commander in terms of bias on recovered $r$ for complex spectral models (power-law and curved power-law) of the synchrotron emission and complex dust models (dust decorrelation). Assuming 84 % delensing, we can achieve an improvement of $\sigma (r = 0)$ by approximately 50 % as compared to the results obtained for the same configuration without any lensing correction., Comment: 17 pages, 12 figures, Published in MNRAS

The largest fluctuation in the CMB sky is the CMB dipole, which is believed to be caused by the motion of our observation frame with respect to the CMB rest frame. This motion accounts for the known motion of the Solar System barycentre with a best-fit amplitude of $369$ km/s, in the direction ($\ell= 264^\circ$, $b=48^\circ$) in galactic coordinates. Along with the CMB dipole signal, this motion also causes an inevitable signature of statistical anisotropy in the higher multipoles due to the modulation and aberration of the CMB temperature and polarization fields. This leads to a correlation between adjacent CMB multipoles causing a non-zero value of the off-diagonal terms in the covariance matrix which can be captured in terms of the dipolar spectra of the bipolar spherical harmonics (BipoSH). In our work, we jointly infer the CMB power spectrum and the BipoSH spectrum in a Bayesian framework using the $\textit{Planck}$-2018 $\texttt{SMICA}$ temperature map. We detect amplitude and direction of the local motion consistent with the canonical value $v=369$ km/s inferred from CMB dipole with a statistical significance of $4.54\sigma$, $4.97\sigma$ and $5.23\sigma$ respectively from the masked temperature map with the available sky fraction $40.1\%$, $59.1\%$, and $72.2\%$, confirming the common origin of both the signals. The Bayes factor in favor of the canonical value is between $7$ to $8$ depending on the choice of mask. But it strongly disagrees (by a value of the Bayes factor about $10^{-10}-10^{-11}$) with a higher value of local motion which one can infer from the amplitude of the dipole signal obtained from the CatWISE2020 quasar catalog using the WISE and NEOWISE data set., Comment: 23 pages, 7 figures, 1 table; matches with the accepted version

We use the modified Richardson-Lucy deconvolution algorithm to reconstruct the Primordial Power Spectrum from the Weak Lensing Power spectrum reconstructed from the CMB anisotropies. This provides an independent window to observe and constrain the PPS $P_R(k)$ along different $k$ scales as compared to CMB Temperature Power Spectrum. The Weak Lensing Power spectrum does not contain secondary variations in power and hence is cleaner, unlike the Temperature Power spectrum which suffers from lensing which is visible in its PPS reconstructions. We demonstrate that the physical behaviour of the weak lensing kernel is different from the temperature kernel and reconstructs broad features over $k$. We provide an in-depth analysis of the error propagation using simulated data and Monte-Carlo sampling, based on Planck best-fit cosmological parameters to simulate the data and cosmic variance limited error bars. The error and initial condition analysis provides a clear picture of the optimal reconstruction region for the estimator and we provide and algorithm for $P_R(k)$ sampling to be used based on the given data, errors and its binning properties. Eventually we plan to use this method on actual mission data and provide a cross reference to PPS reconstructed from other sectors and any possible features in them., Comment: 28 pages, 21 figures, 6 tables

We explore a class of primordial power spectra that can fit the observed anisotropies in the cosmic microwave background well and that predicts a value for the Hubble parameter consistent with the local measurement of $H_0 = 74$ km/s/Mpc. This class of primordial power spectrum consists of a continuous deformation between the best-fit power law primordial power spectrum and the primordial power spectrum derived from the modified Richardson-Lucy deconvolution algorithm applied to the $C_\ell$s of best-fit power law primordial power spectrum. We find that linear interpolation half-way between the power law and modified Richardson-Lucy power spectra fits the Planck data better than the best-fit $\Lambda$CDM by $\Delta\log\mathcal{L} = 2.5$. In effect, this class of deformations of the primordial power spectra offer a new dimension which is correlated with the Hubble parameter. This correlation causes the best-fit value for $H_0$ to shift and the uncertainty to expand to $H_0 = 70.2 \pm 1.2$ km/s/Mpc. When considering the Planck dataset combined with the Cepheid $H_0$ measurement, the best-fit $H_0$ becomes $H_0 = 71.8 \pm 0.9$ km/s/Mpc. We also compute a Bayes factor of $\log K = 5.7$ in favor of the deformation model., Comment: 6 pages, 4 figures

This paper discusses the science case for a sensitive spectro-polarimetric survey of the microwave sky. Such a survey would provide a tomographic and dynamic census of the three-dimensional distribution of hot gas, velocity flows, early metals, dust, and mass distribution in the entire Hubble volume, exploit CMB temperature and polarisation anisotropies down to fundamental limits, and track energy injection and absorption into the radiation background across cosmic times by measuring spectral distortions of the CMB blackbody emission. In addition to its exceptional capability for cosmology and fundamental physics, such a survey would provide an unprecedented view of microwave emissions at sub-arcminute to few-arcminute angular resolution in hundreds of frequency channels, a data set that would be of immense legacy value for many branches of astrophysics. We propose that this survey be carried-out with a large space mission featuring a broad-band polarised imager and a moderate resolution spectro-imager at the focus of a 3.5m aperture telescope actively cooled to about 8K, complemented with absolutely-calibrated Fourier Transform Spectrometer modules observing at degree-scale angular resolution in the 10-2000 GHz frequency range. We propose two observing modes: a survey mode to map the entire sky as well as a few selected wide fields, and an observatory mode for deeper observations of regions of specific interest., Comment: 20 pages, white paper submitted in answer to the "Voyage 2050" call to prepare the long term plan in the ESA science programme

The primary source of systematic uncertainty in the quest for the B-mode polarization of the Cosmic Microwave Background (CMB) introduced by primordial gravitational waves is polarized thermal emission from Galactic dust. Therefore, accurate characterization and separation of the polarized thermal dust emission is an essential step in distinguishing such a faint CMB B-mode signal. We provide a modelling framework to simulate polarized thermal dust emission based on the model described in Ghosh et al. (2017), making use of both the Planck dust and Effelsberg-Bonn HI surveys over the northern Galactic cap. Our seven-parameter dust model, incorporating both HI gas in three different column density templates as a proxy for spatially variable dust intensity and a phenomenological model of Galactic magnetic field, is able to reproduce both 1- and 2-point statistics of the observed dust polarization maps seen by Planck at 353 GHz over a selected low-column density region in the northern Galactic cap. This work has important applications in assessing the accuracy of component separation methods and in quantifying the confidence level of separating polarized Galactic emission and the CMB B-mode signal, as is needed for ongoing and future CMB missions., Comment: 12 pages, 12 figures, Accepted in A&A

Cosmic microwave background measurements show an agreement with the concordance cosmology model except for a few notable anomalies: Power Suppression, the lack of large scale power in the temperature data compared to what is expected in the concordance model, and Cosmic Hemispherical Asymmetry, a dipolar breakdown of statistical isotropy. An expansion of the CMB covariance in Bipolar Spherical Harmonics naturally parametrizes both these large-scale anomalies, allowing us to perform an exhaustive, fully Bayesian joint analysis of the power spectrum and violations of statistical isotropy up to the dipole level. Our analysis sheds light on the scale dependence of the Cosmic Hemispherical Asymmetry. Assuming a scale-dependent dipole modulation model with a two-parameter power law form, we explore the posterior pdf of amplitude $A(l = 16)$ and the power law index $\alpha$ and find the maximum a posteriori values $A_*(l = 16) = 0.064 \pm 0.022$ and $\alpha_* = -0.92 \pm 0.22$. The maximum a posteriori direction associated with the Cosmic Hemispherical Asymmetry is $(l,b) = (247.8^o, -19.6^o)$ in Galactic coordinates, consistent with previous analyses. We evaluate the Bayes factor $B_{SI-DM}$ to compare the Cosmic Hemispherical Asymmetry model with the isotropic model. The data prefer but do not substantially favor the anisotropic model ($B_{SI-DM}=0.4$). We consider several priors and find that this evidence ratio is robust to prior choice. The large-scale power suppression does not soften when jointly inferring both the isotropic power spectrum and the parameters of the asymmetric model, indicating no evidence that these anomalies are coupled., Comment: 38 pages and 15 figures; matches with the accepted version

We discuss the discordance between the estimated values of the cosmological parameters from Planck assuming the concordance $\Lambda$CDM model and low-redshift measurements. In particular, we consider the Hubble constant mismatch between Planck temperature constraint for the $\Lambda$CDM model and the Riess et. al. local measurements as well as the discordance between the estimated value of $S_8$ from Planck and some weak lensing surveys such as Kilo Degree Survey (KiDS-450) and Dark Energy Survey (DES) observations. The discordance can come from a wide range of non-standard cosmological or astrophysical processes as well as from some particular systematics of the observations. In this paper, without considering any particular astrophysical process or extension to the standard model at the background level, we seek solely to project the effect of these differences in the values of the key cosmological parameters on to the shape of the primordial power spectrum (PPS). In order to realise this goal, we uncover the shape of the PPS by implementing the Modified Richardson-Lucy algorithm (MRL) that fits the Planck temperature data as acceptably as the case of the standard model of cosmology, but with a Hubble constant consistent with local measurements as well as improving the consistency between the derived $S_8$ and $\sigma_8$ parameters with estimations of the weak lensing surveys., Comment: 6 pages, 4 figures

We consider the possibility that the primordial curvature perturbation is direction-dependent. To first order this is parameterised by a quadrupolar modulation of the power spectrum and results in statistical anisotropy of the CMB, which can be quantified using `bipolar spherical harmonics'. We compute these for the Planck DR2-2015 SMICA map and estimate the noise covariance from Planck Full Focal Plane 9 simulations. A constant quadrupolar modulation is detected with 2.2 sigma significance, dropping to 2 sigma when the primordial power is assumed to scale with wave number k as a power law. Going beyond previous work we now allow the spectrum to have arbitrary scale-dependence. Our non-parametric reconstruction then suggests several spectral features, the most prominent at k ~ 0.006/Mpc. When a constant quadrupolar modulation is fitted to data in the range 0.005 < k Mpc < 0.008, its preferred directions are found to be related to the cosmic hemispherical asymmetry and the CMB dipole. To determine the significance we apply two test statistics to our reconstructions of the quadrupolar modulation from data, against reconstructions of realisations of noise only. With a test statistic sensitive only to the amplitude of the modulation, the reconstructions from the multipole range 30 < l < 1200 are unusual with 2.1 sigma significance. With the second test statistic, sensitive also to the direction, the significance rises to 6.9 sigma. Our approach is easily generalised to include other data sets such as polarisation, large-scale structure and forthcoming 21-cm line observations which will enable these anomalies to be investigated further., Comment: 41 pages, 28 figures, 11 tables; Substantially revised considering full noise covariance matrix for masked sky (no 'diagonal approximation' as in previous work); Increased detection significance for scale-dependent quadrupolar modulation which for low k is aligned with the cosmic hemispherical asymmetry; Accepted for publication in JCAP

We report an improved technique for diffuse foreground minimization from Cosmic Microwave Background (CMB) maps using a new multi-phase iterative internal-linear-combination (ILC) approach in harmonic space. The new procedure consists of two phases. In phase 1, a diffuse foreground cleaned map is obtained by performing a usual ILC operation in the harmonic space in a single iteration over the desired portion of the sky. In phase 2, we obtain the final foreground cleaned map using an iterative ILC approach also in the harmonic space, however, now, during each iteration of foreground minimization, some of the regions of the sky that are not being cleaned in the current iteration, are replaced by the corresponding cleaned portions of the phase 1 cleaned map. The new ILC method nullifies a foreground leakage signal that is otherwise inevitably present in the old and usual harmonic space iterative ILC method. The new method is flexible to handle input frequency maps, irrespective of whether or not they initially have the same instrumental and pixel resolution, by bringing them to a common and maximum possible beam and pixel resolution at the beginning of the analysis. This dramatically reduces data redundancy and hence memory usage and computational cost. During the ILC weight calculation it avoids any need to deconvolve partial sky spherical harmonic coefficients by the beam and pixel window functions, which in strict mathematical sense, is not well-defined for azimuthally symmetric window functions. Using WMAP 9-year and Planck-2015 published frequency maps we obtain a pair of foreground cleaned CMB maps and CMB angular power spectrum. Our power spectrum match well with Planck-2015 results, with some difference. Finally, we show that the weights for ILC foreground minimization have an intrinsic characteristic that it tends to produce a statistically isotropic CMB map as well., Comment: 17 pages, 17 figures

Motivated by Planck confirmation of an anomalously low value of the CMB temperature fluctuations up to multipole $\ell<40$, we in this paper try to explain such feature by investigating case of punctuated inflation scenario. This form of inflation potential is inspired by Minimal Super-symmetric Standard Model (MSSM) wherein suppression of curvature perturbation power at large scales is produced by introducing period of fast-roll phase of the inflation sandwiched between two stages of slow-roll phase. We apply Markov Chain Monte Carlo analysis to determine posterior distribution and the best fit values of the model parameters using recent WMAP9 and Planck data. We show that WMAP9 and Planck results are consistent with each other and that with Planck data we obtain tighter constraints for punctuated inflation parameters. We find that punctuated inflation leads to better fit in CMB data compared to simple power law model. The improvement in the fit to the WMAP9 data is $\Delta \chi^2\sim 3.6$ and for Planck the improvement is $\Delta \chi^2\sim 5.4$. We find that $AIC$ does not discriminate between punctuated inflation and simple power law model for WMAP9 data. However, for Planck data we find that punctuated inflation is moderately preferred over a simple power law model., Comment: 18 pages, 6 figures, 3 tables, Accepted in JCAP

A stochastic gravitational wave background (SGWB) will affect the CMB anisotropies via weak lensing. Unlike weak lensing due to large scale structure which only deflects photon trajectories, a SGWB has an additional effect of rotating the polarization vector along the trajectory. We study the relative importance of these two effects, deflection \& rotation, specifically in the context of E-mode to B-mode power transfer caused by weak lensing due to SGWB. Using weak lensing distortion of the CMB as a probe, we derive constraints on the spectral energy density ($\Omega_{GW}$) of the SGWB, sourced at different redshifts, without assuming any particular model for its origin. We present these bounds on $\Omega_{GW}$ for different power-law models characterizing the SGWB, indicating the threshold above which observable imprints of SGWB must be present in CMB., Comment: 12 pages, 3 figures, Matches the published version

Mild, unavoidable deviations from circular-symmetry of instrumental beams along with scan strategy can give rise to measurable Statistical Isotropy (SI) violation in Cosmic Microwave Background (CMB) experiments. If not accounted properly, this spurious signal can complicate the extraction of other SI violation signals (if any) in the data. However, estimation of this effect through exact numerical simulation is computationally intensive and time consuming. A generalized analytical formalism not only provides a quick way of estimating this signal, but also gives a detailed understanding connecting the leading beam anisotropy components to a measurable BipoSH characterisation of SI violation. In this paper, we provide an approximate generic analytical method for estimating the SI violation generated due to a non-circular (NC) beam and arbitrary scan strategy, in terms of the Bipolar Spherical Harmonic (BipoSH) spectra. Our analytical method can predict almost all the features introduced by a NC beam in a complex scan and thus reduces the need for extensive numerical simulation worth tens of thousands of CPU hours into minutes long calculations. As an illustrative example, we use WMAP beams and scanning strategy to demonstrate the easability, usability and efficiency of our method. We test all our analytical results against that from exact numerical simulations., Comment: 25 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1210.7318

Any isotropy violating phenomena on cosmic microwave background (CMB) induces off-diagonal correlations in the two-point function. These correlations themselves can be used to estimate the underlying anisotropic signals. Masking due to residual foregrounds, or availability of partial sky due to survey limitation, are unavoidable circumstances in CMB studies. But, masking induces additional correlations, and thus complicates the recovery of such signals. In this work, we discuss a procedure based on bipolar spherical harmonic (BipoSH) formalism to comprehensively addresses any spurious correlations induced by masking and successfully recover hidden signals of anisotropy in observed CMB maps. This method is generic, and can be applied to recover a variety of isotropy violating phenomena. Here, we illustrate the procedure by recovering the subtle Doppler boost signal from simulated boosted CMB skies, which has become possible with the unprecedented full-sky sensitivity of PLANCK probe., Comment: Submitted to Proceeding of 11th Rencontres du Vietnam on Cosmology - 50 years after CMB discovery, Quy Nhon, Vietnam (August 16-22, 2015)

Persistent evidence for a cosmic hemispherical asymmetry in the temperature field of cosmic microwave background (CMB) as observed by both WMAP as well as PLANCK increases the possibility of its cosmological origin. Presence of this signal may lead to different values for the standard model cosmological parameters in different directions, and that can have significant implications for other studies where they are used. We investigate the effect of this cosmic hemispherical asymmetry on cosmological parameters using non-isotropic Gaussian random simulations injected with both scale dependent and scale independent modulation strengths. Our analysis shows that $A_s$ and $n_s$ are the most susceptible parameters to acquire position dependence across the sky for the kind of isotropy breaking phenomena under study. As expected, we find maximum variation arises for the case of scale independent modulation of CMB anisotropies. We find that scale dependent modulation profile as seen in PLANCK data could lead to only $1.25\sigma$ deviation in $A_s$ in comparison to its estimate from isotropic CMB sky., Comment: 14 pages, 5 figures. Matches the published version

We present a general method for Bayesian inference of the underlying covariance structure of random fields on a sphere. We employ the Bipolar Spherical Harmonic (BipoSH) representation of general covariance structure on the sphere. We illustrate the efficacy of the method as a principled approach to assess violation of statistical isotropy (SI) in the sky maps of Cosmic Microwave Background (CMB) fluctuations. SI violation in observed CMB maps arise due to known physical effects such as Doppler boost and weak lensing; yet unknown theoretical possibilities like cosmic topology and subtle violations of the cosmological principle, as well as, expected observational artefacts of scanning the sky with a non-circular beam, masking, foreground residuals, anisotropic noise, etc. We explicitly demonstrate the recovery of the input SI violation signals with their full statistics in simulated CMB maps. Our formalism easily adapts to exploring parametric physical models with non-SI covariance, as we illustrate for the inference of the parameters of a Doppler boosted sky map. Our approach promises to provide a robust quantitative evaluation of the evidence for SI violation related anomalies in the CMB sky by estimating the BipoSH spectra along with their complete posterior., Comment: 16 pages, 6 figures

Recent measurements of the temperature field of Cosmic Microwave Background (CMB) provide tantalising evidence for violation of Statistical Isotropy (SI) that constitutes a fundamental tenet of contemporary cosmology. CMB space based missions, WMAP and Planck have observed a $7\%$ departure in the SI temperature field at large angular scales. However, due to higher cosmic variance at low multipoles, the significance of this measurement is not expected to improve from any future CMB temperature measurements. We demonstrate that weak lensing of the CMB due to scalar perturbations produce a corresponding SI violation in $B$ modes of CMB polarization at smaller angular scales. Measurability of this phenomenon depends upon the scales ($l$ range) over which power asymmetry is present. Power asymmetry which is restricted only to $l<64$ in temperature field cannot lead to any significant observable effect from this new window. However, this effect can put an independent bound on the spatial range of scales of hemispherical asymmetry present in scalar sector., Comment: 7 pages, 2 figures. Matches the published version

The Bipolar Spherical Harmonics (BipoSH) form a natural basis to study the CMB two point correlation function in a non-statistically isotropic (non-SI) universe. The coefficients of expansion in this basis are a generalisation of the well known CMB angular power spectrum and contain complete information of the statistical properties of a non-SI but Gaussian random CMB sky. We use these coefficients to describe the weak lensing of CMB photons in a non-SI universe. Finally we show that the results reduce to the standard weak lensing results in the isotropic limit., Comment: 16 pages

Statistical isotropy (SI) is one of the fundamental assumptions made in cosmological model building. This assumption is now being rigorously tested using the almost full sky measurements of the CMB anisotropies. A major hurdle in any such analysis is to handle the large biases induced due to the process of masking. We have developed a new method of analysis, using the bipolar spherical harmonic basis functions, in which we semi-analytically evaluate the modifications to SI violation induced by the mask. The method developed here is generic and can be potentially used to search for any arbitrary form of SI violation. We specifically demonstrate the working of this method by recovering the Doppler boost signal from a set of simulated, masked CMB skies., Comment: 8 pages, 3 figures

The recent measurements of temperature and polarization of Cosmic Microwave Background (CMB) have improved our understanding of the Universe and are in remarkable agreement with the $\Lambda$CDM cosmological model. However, scale dependent features like power suppression in the angular power spectrum and Cosmic Hemispherical Asymmetry (CHA) in the temperature field of CMB at large angular scales, hinting at possible departure from the $\Lambda$CDM model persist in the CMB data. In this paper we present a physical mechanism linked to possible initial inhomogeneities in the inflationary scalar field that could generate CHA in both scalar and tensor sector within the frame work of single field inflationary model with an initial fast-roll phase. The modulation amplitude of CHA in both scalar and tensor perturbations are related and depend upon the initial shape of the inflaton potential. By using the observed value of CHA and obeying the isotropy of the temperature field of CMB, we obtain the theoretical upper bound on the amplitude of CHA for tensor perturbations within the framework of single field initial fast roll inflation models. The bound indicates that a maximum of $0.05\%$ modulation in tensor sector is possible and hence within the measurability of future mission, tensor perturbations should be statistically isotropic., Comment: 15 pages, 3 figures

The remarkable progress in cosmic microwave background (CMB) studies over past decade has led to the era of precision cosmology in striking agreement with the $\Lambda$CDM model. However, the lack of power in the CMB temperature anisotropies at large angular scales (low-$\ell$), as has been confirmed by the recent Planck data also (up to $\ell=40$), although statistically not very strong (less than $3\sigma$), is still an open problem. One can avoid to seek an explanation for this problem by attributing the lack of power to cosmic variance orcan look for explanations i.e., different inflationary potentials or initial conditions for infl ation to begin with, non-trivial topology, ISW effect etc. Features in the primordial power spectrum (PPS) motivated by the early universe physics has been the most common solution to address this problem. In the present work we also follow this approach and consider a set of PPS which have features and constrain the parameters of those using WMAP 9 year and Planck data employing Markov-Chain Monte Carlo (MCMC) analysis. The prominent feature of all the models of PPS that we consider is an infra-red cut off which leads to suppression of power at large angular scales. We consider models of PPS with maximum three extra parameters and use Akaike information criterion ($AIC$) and Bayesian information criterion ($BIC$) of model and Bayesian information criterion ($BIC$) of model selection to compare the models. For most models, we find good constraints for the cut off scale $k_c$, however, for other parameters our constraints are not that good. We find that sharp cut off model gives best likelihood value for the WMAP 9 year data, but is as good as power law model according to $AIC$. For the joint WMAP 9+Planck data set, Starobinsky model is slightly preferred by $AIC$ which is also able to produce CMB power suppression up to $\ell\leq30$ to some extent., Comment: 27 pages, 10 figures, 3 tables, matches with the published version, abstract is shortened to keep it within arXiv's limit (1920 characters)

Estimation of the angular power spectrum is one of the important steps in Cosmic Microwave Background (CMB) data analysis. Here, we present a nonparametric estimate of the temperature angular power spectrum for the Planck 2013 CMB data. The method implemented in this work is model-independent, and allows the data, rather than the model, to dictate the fit. Since one of the main targets of our analysis is to test the consistency of the $\Lambda$CDM model with Planck 2013 data, we use the nuisance parameters associated with the best-fit $\Lambda$CDM angular power spectrum to remove foreground contributions from the data at multipoles $\ell \geq50$. We thus obtain a combined angular power spectrum data set together with the full covariance matrix, appropriately weighted over frequency channels. Our subsequent nonparametric analysis resolves six peaks (and five dips) up to $\ell \sim1850$ in the temperature angular power spectrum. We present uncertainties in the peak/dip locations and heights at the $95\%$ confidence level. We further show how these reflect the harmonicity of acoustic peaks, and can be used for acoustic scale estimation. Based on this nonparametric formalism, we found the best-fit $\Lambda$CDM model to be at $36\%$ confidence distance from the center of the nonparametric confidence set -- this is considerably larger than the confidence distance ($9\%$) derived earlier from a similar analysis of the WMAP 7-year data. Another interesting result of our analysis is that at low multipoles, the Planck data do not suggest any upturn, contrary to the expectation based on the integrated Sachs-Wolfe contribution in the best-fit $\Lambda$CDM cosmology., Comment: 15 pages, 8 figures, 2 tables

Cosmic Microwave Background (CMB) is an important probe for understanding the inflationary era of the Universe. We consider the Perturbed Power Law (PPL) model of inflation which is a soft deviation from Power Law (PL) inflationary model. This model captures the effect of higher order derivative of Hubble parameter during inflation, which in turn leads to a non-zero effective mass $m_{\rm eff}$ for the inflaton field. The higher order derivatives of Hubble parameter at leading order sources constant difference in the spectral index for scalar and tensor perturbation going beyond PL model of inflation. PPL model have two observable independent parameters, namely spectral index for tensor perturbation $\nu_t$ and change in spectral index for scalar perturbation $\nu_{st}$ to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard $\Lambda$CDM model. Although BICEP-2 claimed a detection of $r=0.2$, estimates of dust contamination provided by Planck have left open the possibility that only upper bound on $r$ will be expected in a joint analysis. As a result we consider different upper bounds on the value of $r$ and show that PPL model can explain a lower value of tensor to scalar ratio ($r<0.1$ or $r<0.01$) for a scalar spectral index of $n_s=0.96$ by having a non-zero value of effective mass of the inflaton field $\frac{m^2_{\rm eff}}{H^2}$. The analysis with WP+ Planck likelihood shows a non-zero detection of $\frac{m^2_{\rm eff}}{H^2}$ with $5.7\,\sigma$ and $8.1\,\sigma$ respectively for $r<0.1$ and $r<0.01$. Whereas, with BICEP-2 likelihood $\frac{m^2_{\rm eff}}{H^2} = -0.0237 \pm 0.0135$ which is consistent with zero., Comment: 11 Pages, 4 Figures. Matches the published version

The two point correlation function of the CMB temperature anisotropies is generally assumed to be statistically isotropic (SI). Deviations from this assumption could be traced to physical or observational artefacts and systematic effects. Measurement of non-vanishing power in the BipoSH spectra is a standard statistical technique to search for isotropy violations. Although this is a neat tool allowing a blind search for SI violations in the CMB sky, it is not easy to discern the cause of isotropy violation using this measure. In this article, we propose a novel technique of constructing orthogonal BipoSH estimators, which can be used to discern between models of isotropy violation.

Using modified Richardson-Lucy algorithm we reconstruct the primordial power spectrum (PPS) from Planck Cosmic Microwave Background (CMB) temperature anisotropy data. In our analysis we use different combinations of angular power spectra from Planck to reconstruct the shape of the primordial power spectrum and locate possible features. Performing an extensive error analysis we found the dip near $\ell\sim750-850$ represents the most prominent feature in the data. Feature near $\ell\sim1800-2000$ is detectable with high confidence only in 217 GHz spectrum and is apparently consequence of a small systematic as described in the revised Planck 2013 papers. Fixing the background cosmological parameters and the foreground nuisance parameters to their best fit baseline values, we report that the best fit power law primordial power spectrum is consistent with the reconstructed form of the PPS at 2$\sigma$ C.L. of the estimated errors (apart from the local features mentioned above). As a consistency test, we found the reconstructed primordial power spectrum from Planck temperature data can also substantially improve the fit to WMAP-9 angular power spectrum data (with respect to power-law form of the PPS) allowing an overall amplitude shift of $\sim2.5\%$. In this context low-$\ell$ and 100 GHz spectrum from Planck which have proper overlap in the multipole range with WMAP data found to be completely consistent with WMAP-9 (allowing amplitude shift). As another important result of our analysis we do report the evidence of gravitational lensing through the reconstruction analysis. Finally we present two smooth form of the PPS containing only the important features. These smooth forms of PPS can provide significant improvements in fitting the data (with respect to the power law PPS) and can be helpful to give hints for inflationary model building., Comment: 30 pages, 11 figures, 1 table, matches published version in JCAP

Estimation of parameters of the \lq standard\rq \,model of cosmology have dramatically improved over past few decades due to increasingly exquisite measurements made by Cosmic Microwave Background (CMB) experiments. Recent data from Planck matches well with the minimal $\Lambda$CDM model. A likelihood analysis using Planck, WMAP and a selection of high resolution experiments (highL), tensor to scalar ratio $r_{0.002}$ is found to be $<0.11$ when $dn_{s}/d\ln k = 0$. Planck also imposes an upper bound on neutrino mass $\sum m_\nu<0.23\,$eV using Planck+WMAP+highL+BAO likelihood. However, recently results from BICEP 2 claims the detection of $r= 0.2^{+0.07}_{-0.05}$ from polarization spectra. Further, results from SDSS-III BOSS large scale galaxy survey constrains the total neutrino mass to $\sum m_\nu=0.36 \pm 0.10$ eV. It is important to study the consequences of these new measurements on other cosmological parameters. In this paper we assess the revised constraints on cosmological parameters in light of these two measurements that are in some tension with the constraints from Planck. Using the prior on $\sum m_\nu$ as measured by SDSS-III BOSS and BICEP 2 likelihood, we find that the model with running spectral index ($dn_{s}/d\ln k \neq 0$) leads to a value of $A_L>1$ at $3.1 \sigma$. But, the model with $dn_{s}/d\ln k =0$ makes $A_L$ consistent with $1$, at $2.1\sigma$ and also shows that $N_{\rm eff}$ is consistent with its theoretical value of $3.046$ at around $2\sigma$. Therefore, the analysis in this paper shows that the model with $dn_{s}/d\ln k =0$ gives consistency with other cosmological parameters ($N_{\rm eff}$ and $A_L$ ) when the current limits on $\sum m_\nu$ and $r_{0.05}$ are considered. However, on reducing the value of $r_{0.05}$, the model with non-zero $dn_{s}/d\ln k$ gives consistent result of $A_L =1$ [abridged]., Comment: 14 pages, 10 figures. Matches the published version

Markov Chain Monte Carlo (MCMC) sampler is widely used for cosmological parameter estimation from CMB and other data. However, due to the intrinsic serial nature of the MCMC sampler, convergence is often very slow. Here we present a fast and independently written Monte Carlo method for cosmological parameter estimation named as Slick Cosmological Parameter Estimator (SCoPE), that employs delayed rejection to increase the acceptance rate of a chain, and pre-fetching that helps an individual chain to run on parallel CPUs. An inter-chain covariance update is also incorporated to prevent clustering of the chains allowing faster and better mixing of the chains. We use an adaptive method for covariance calculation to calculate and update the covariance automatically as the chains progress. Our analysis shows that the acceptance probability of each step in SCoPE is more than $95\%$ and the convergence of the chains are faster. Using SCoPE, we carry out some cosmological parameter estimations with different cosmological models using WMAP-9 and Planck results. One of the current research interests in cosmology is quantifying the nature of dark energy. We analyze the cosmological parameters from two illustrative commonly used parameterisations of dark energy models. We also asses primordial helium fraction in the universe can be constrained by the present CMB data from WMAP-9 and Planck. The results from our MCMC analysis on the one hand helps us to understand the workability of the SCoPE better, on the other hand it provides a completely independent estimation of cosmological parameters from WMAP-9 and Planck data., Comment: 22 pages, 10 figures, 2 tables

Statistical isotropy (SI) of Cosmic Microwave Background (CMB) fluctuations is a key observational test to validate the cosmological principle underlying the standard model of cosmology. While a detection of SI violation would have immense cosmological ramification, it is important to recognise their possible origin in systematic effects of observations. WMAP seven year (WMAP-7) release claimed significant deviation from SI in the bipolar spherical harmonic (BipoSH) coefficients $A_{ll}^{20}$ and $A_{l-2l}^{20}$. Here we present the first explicit reproduction of the measurements reported in WMAP-7, confirming that beam systematics alone can completely account for the measured SI violation. The possibility of such a systematic origin was alluded to in WMAP-7 paper itself and other authors but not as explicitly so as to account for it accurately. We simulate CMB maps using the actual WMAP non-circular beams and scanning strategy. Our estimated BipoSH spectra from these maps match the WMAP-7 results very well. It is also evident that only a very careful and adequately detailed modelling, as carried out here, can conclusively establish that the entire signal arises from non-circular beam effect. This is important since cosmic SI violation signals are expected to be subtle and dismissing a large SI violation signal as observational artefact based on simplistic plausibility arguments run the serious risk of "throwing the baby out with the bathwater"., Comment: 4 pages, 3 figures. Published version. Includes major revision in the text and one important figure. No change in the results

Recent results of Planck data reveal that the power in the low multipoles of the CMB angular power spectrum, approximately up to $l=30$, is significantly lower than the theoretically predicted in the best fit $\Lambda$CDM model. In this paper we investigate the possibility of invoking the Integrated Sachs-Wolfe (ISW) effect to explain this power deficit at low multipoles. The ISW effect that originates from the late time expansion history of the universe is rich in possibilities given the limited understanding of the origin of dark energy (DE). It is a common understanding that the ISW effect adds to the power at the low multipoles of the CMB angular power spectrum. In this paper we carry out an analytic study to show that there are some expansion histories in which the ISW effect, instead of adding power, provides negative contribution to the power at low multipoles. Guided by the analytic study, we present examples of the features required in the late time expansion history of the universe that could explain the power deficiency through the ISW effect. We also show that an ISW origin of power deficiency is consistent, at present, with other cosmological observations that probe the expansion history such as distance modulus, matter power spectrum and the evolution of cluster number count. We also show that the ISW effect may be distinguished from power deficit originating from features in the PPS using the measurements of the CMB polarization spectrum at low multipoles expected from Planck. We conclude that the power at low multipoles of the CMB anisotropy could well be closely linked to Dark Energy puzzle in cosmology and this observation could be actually pointing to richer phenomenology of DE beyond the cosmological constant $\Lambda$. (abbreviated), Comment: 20 pages, 7 figures

Although theoretically expected to be Statistically Isotropic (SI), the observed Cosmic Microwave Background (CMB) temperature \& polarization field would exhibit SI violation due to various inevitable effects like weak lensing, Doppler boost and practical limitations of observations like non-circular beam, masking etc. However, presence of any SI violation beyond these effects may lead to a discovery of inherent cosmic SI violation in the CMB temperature \& polarization field. Recently, Planck presented strong evidence of SI violation as a dipolar power asymmetry of the CMB temperature field in two hemispheres. Statistical studies of SI violation effect require non-SI (nSI) Gaussian realizations of CMB temperature field. The nSI Gaussian temperature field leads to non-zero off-diagonal terms in the Spherical Harmonics (SH) space covariance matrix encoded in the coefficients of the Bipolar Spherical Harmonics (BipoSH) representation. We discuss an effective numerical algorithm, Code for Non-Isotropic Gaussian Sky (CoNIGS) to generate nSI realizations of Gaussian CMB temperature field of Planck like resolution with specific cases of SI violation. Realizations of nSI CMB temperature field are obtained for non-zero quadrupolar $(L=2)$ BipoSH measurements by WMAP, dipolar asymmetry (resembles $L=1$ BipoSH coefficients) with a \emph{scale dependent} modulation field as measured by Planck and for Doppler boosted CMB temperature field which also leads to $L=1$ BipoSH spectra. Our method, CoNIGS can incorporate any kind of SI violation and can produce nSI realizations efficiently., Comment: 18 pages, 14 figures. Matches the published version

Precise measurements of the Cosmic Microwave Background (CMB) anisotropy have been one of the foremost concerns in modern cosmology as it provides valuable information on the cosmology of the universe. However, an accurate estimation of the CMB power spectrum faces many challenges as the CMB experiments sensitivity increases. Furthermore, for polarization experiments the precision of measurement is complicated by the fact that the polarisation signal is very faint compared to the measured total intensity, and could be impossible to detect in the presence of high level of systematics. One of the most important source of errors in CMB polarization experiment is the beam asymmetry. For large data set the estimation of the CMB polarization power spectrum with standard optimal Maximum Likelihood (ML) is prohibitive for high resolution CMB experiments due to the enormous required computation time. In this paper, we present a semi-analytical framework using the pseudo-$C_{l}$ estimator to compute the power spectrum TE of the temperature anisotropy and the E-component of the polarization radiation field using non-circular beams. We adopt a model of beams obtained from a perturbative expansion of the beam around a circular (axisymmetric) one in harmonic space, and compute the resulting bias matrix which relates the true power spectrum with the observed one using an efficient algorithm for rapid computation. We show that for a multipole up to $l_{max}=500$, the bias matrix can be computed in less than one second with a single CPU processor at 2.53 GHz. We find that the uncertainties induced by the beam asymmetry in the polarization power spectrum at the peak of the bias matrix for WMAP and Planck experiments can be as large as a few 10 to 20% (upper limit for Planck LFI 30 GHz), Comment: 25 pages, 24 figures

In the frame of a moving observer, the Cosmic Microwave Background (CMB) fluctuation exhibits violation of Statistical Isotropy (SI). The SI violation effect from our local motion on CMB temperature fluctuation has been measured in the recent Planck results. We calculate the effect of our local motion with velocity $(\beta \equiv |\boldsymbol v|/c= 1.23 \times 10^{-3})$ on CMB polarization field. The Lorentz transformation of the polarization field leads to aberration in the direction of incoming photons and also modulation of the Stokes parameters, which results in mixing of power between different CMB multipoles. We show that for small values of $\beta$, the effect on the angular power spectra that corresponds to the diagonal terms in the spherical harmonic space is at $O(\beta^2)$. But non-zero off-diagonal terms at the linear order in $\beta$ could provide a measurable signature of SI violation in the Bipolar Spherical Harmonic (BipoSH) representation. We also calculate the measurability of $\beta$ from polarization maps from experiments like Planck and PRISM. It is possible to measure $\beta$ from the ideal, cosmic variance limited BipoSH spectra of $EE$, $TE$, $BB$, but not in $EB$ and $TB$. With the instrumental noise of and angular resolution of Planck, it is not possible to measure $\beta$ with high statistical significance from BipoSH spectra of polarization. PRISM can measure $\beta$ with high significance in both $EE$ and $TE$ BipoSH spectra, but not in $BB$, $EB$ and $TB$ BipoSH spectra., Comment: 26 pages, 4 figures. Matches the published version

We provide a detailed treatment and comparison of the weak lensing effects due to large-scale structure (LSS), or scalar density perturbations and those due to gravitational waves(GW) or tensor perturbations, on the temperature and polarization power spectra of the Cosmic Microwave Background (CMB). We carry out the analysis both in real space by using the correlation function method, as well as in the spherical harmonic space. We find an intriguing similarity between the lensing kernels associated with LSS lensing and GW lensing. It is found that the lensing kernels only differ in relative negative signs and their form is very reminiscent of even and odd parity bipolar spherical harmonic coefficients. Through a numerical study of these lensing kernels, we establish that lensing due to GW is more efficient at distorting the CMB spectra as compared to LSS lensing, particularly for the polarization power spectra. Finally we argue that the CMB B-mode power spectra measurements can be used to place interesting constraints on GW energy densities., Comment: Typos corrected. Published : Phys. Rev. D 88, 063507, 4 September 2013

A number of studies of WMAP and Planck have highlighted that the power at the low multipoles in CMB power spectrum are lower than their theoretically predicted values. Possible angular correlation between the orientations of these low multipoles have also been claimed. It is important to investigate the possibility that the power deficiency at low multipoles may not be of primordial origin and is only an observation artifact coming from the scan procedure adapted in the WMAP or Planck satellites. Therefore, its always important to investigate all the observational artifacts that can mimic them. The CMB dipole which is almost 550 times higher than the quadrupole can leak to the higher multipoles due to the non-symmetric beam shape of the WMAP. In this paper a formalism has been developed and simulations are carried out to study the effect of the non-symmetric beam on this power transfer. It is interesting to observed that a small but non-negligible amount of power from the dipole can get transferred to the quadrupole and the higher multipoles due to the non-symmetric beam. It is shown that in case of WMAP scan strategy the shape of the quadrupole coming due to this power leakage is very much similar to the observed quadrupole from WMAP data. Simulations have also been carried out for Planck scan strategy. It is seen that for Planck scan strategy the power transfer is not only limited to the quadrupole but also to a few higher low multipoles. Since the actual beam shapes of Planck are not publicly available we present results in terms of upper limits on asymmetric beam parameters that would contaminate of the quadrupole power at the level of $1\mu K$., Comment: 12 pages, 18 figures

In this paper, using and implementing a new line of sight CMB code, called CMBAns [1], that allows us to modify H(z) for any given feature at any redshift we study the effect of changes in the expansion history of the Universe on the CMB power spectrum. Motivated by the detailed analytical calculations of the effects of the changes in H(z) on ISW plateau and CMB low multipoles, we study two phenomenological parametric form of the expansion history using WMAP data and through MCMC analysis. Our MCMC analysis shows that the standard LCDM cosmological model is consistent with the CMB data allowing the expansion history of the Universe vary around this model at different redshifts. However, our analysis also shows that a decaying dark energy model proposed in [2] has in fact a marginally better fit than the standard cosmological constant model to CMB data. Concordance of our studies here with the previous analysis showing that Baryon Acoustic Oscillation (BAO) and supernovae data (SN Ia) also prefer mildly this decaying dark energy model to LCDM, makes this finding interesting and worth further investigation., Comment: 20 pages, 11 figures, 2 tables, discussions extended, references added, results unchanged, matches final version published in JCAP

Constraints on the main cosmological parameters using CMB or large scale structure data are usually based on power-law assumption of the primordial power spectrum (PPS). However, in the absence of a preferred model for the early universe, this raises a concern that current cosmological parameter estimates are strongly prejudiced by the assumed power-law form of PPS. In this paper, for the first time, we perform cosmological parameter estimation allowing the free form of the primordial spectrum. This is in fact the most general approach to estimate cosmological parameters without assuming any particular form for the primordial spectrum. We use direct reconstruction of the PPS for any point in the cosmological parameter space using recently modified Richardson-Lucy algorithm however other alternative reconstruction methods could be used for this purpose as well. We use WMAP 9 year data in our analysis considering CMB lensing effect and we report, for the first time, that the flat spatial universe with no cosmological constant is ruled out by more than 4\sigma confidence limit without assuming any particular form of the primordial spectrum. This would be probably the most robust indication for dark energy using CMB data alone. Our results on the estimated cosmological parameters show that higher values of baryonic and matter density and lower value of Hubble parameter (in comparison to the estimated values by assuming power-law PPS) is preferred by the data. However, the estimated cosmological parameters by assuming free form of the PPS have overlap at 1\sigma confidence level with the estimated values assuming power-law form of PPS., Comment: 6 pages, 3 figures, discussions extended, results unchanged, matches the final version published in PRD

The Planck mission, designed for making measurements of the cosmic microwave background (CMB) radiation with unprecedented accuracy and angular resolution, is expected to release its first data set in the near future. For the first time in the CMB history, extensive measurements of the CMB polarization will be made available for the entire sky. Such precise and rich data are expected to contain a great wealth of information about the Universe. The information in the CMB data is conveniently represented in terms of angular power spectra for temperature and polarization. A proper estimation of these CMB power spectra from data is the first step in making inferences about the Universe and, in particular, cosmological parameters that govern the Universe. In this paper, we provide forecasts for the $TT$, $EE$, and $TE$ angular power spectra for the Planck mission. Our forecasts are made using synthetic data based on the best-fit $\Lambda$CDM model while conforming to the characteristics and parameters of the Planck mission. We have analysed such synthetic data sets using a nonparametric function estimation formalism that is otherwise asymptotically model-independent. Indeed, the power spectra estimated from such synthetic data turn out to be sufficiently close to the corresponding $\Lambda$CDM spectra. Our analysis further indicates that the three angular power spectra are determined sufficiently well for $2 \le l \lesssim l_{max}$, where $l_{max} = 2500 {($TT$),} 1377 {($EE$), and} 1727 {($TE$)}$ respectively. A signature of reionization is evident in the $EE$ and $TE$ power spectra in the form of a bump at low $l$s ...

We have improved further the error sensitive Richardson-Lucy deconvolution algorithm making it applicable directly on the un-binned measured angular power spectrum of Cosmic Microwave Background observations to reconstruct the form of the primordial power spectrum. This improvement makes the application of the method significantly more straight forward by removing some intermediate stages of analysis allowing a reconstruction of the primordial spectrum with higher efficiency and precision and with lower computational expenses. Applying the modified algorithm we fit the WMAP 9 year data using the optimized reconstructed form of the primordial spectrum with more than 300 improvement in \chi^2 with respect to the best fit power-law. This is clearly beyond the reach of other alternative approaches and reflects the efficiency of the proposed method in the reconstruction process and allow us to look for any possible feature in the primordial spectrum projected in the CMB data. Though the proposed method allow us to look at various possibilities for the form of the primordial spectrum, all having good fit to the data, proper error-analysis is needed to test for consistency of theoretical models since, along with possible physical artefacts, most of the features in the reconstructed spectrum might be arising from fitting noises in the CMB data. Reconstructed error-band for the form of the primordial spectrum using many realizations of the data, all bootstrapped and based on WMAP 9 year data, shows proper consistency of power-law form of the primordial spectrum with the WMAP 9 data at all wave numbers. Including WMAP polarization data in to the analysis have not improved much our results due to its low quality but we expect Planck data will allow us to make a full analysis on CMB observations on both temperature and polarization separately and in combination., Comment: 19 pages, 5 figures, discussions extended, results unchanged, matches the final version published in JCAP. Note: JCAP published version contains minor typesetting errors (introduced by JCAP at the proof stage) in the plot labels

What do the data, as distinguished from cosmological models, tell us about cosmological parameters that determined the model of the universe? In this paper, we address this question in the context of the WMAP angular power spectra for the cosmic microwave background radiation. Nonparametric methods are ideally suited for this purpose because they are model-independent by construction, and therefore allow inferences that are as data-driven as possible. Our analysis is based on a nonparametric fit to the WMAP 7-year power spectrum data, with uncertainties characterized in the form of a high-dimensional confidence set centered at this fit. For the purpose of making inferences about cosmological parameters, we have devised a sampling method to explore the projection of this confidence set around the nonparametric fit, into the space of seven cosmological parameters Omega_b, Omega_c, Omega_Lambda, Omega_k, H_0, n_s, tau). Our sampling method is justified by its computational simplicity, and validated by the fact that well-known degeneracies in this cosmological parameter space are correctly reproduced in our results. Our results show that cosmological parameters are not as tightly constrained by these data alone. However, incorporating additional prior information in the analysis (e.g., constraining the values of H_0 or Omega_k) leads to tighter confidence intervals on parameters that are consistent with uncertainties estimated by the mainstream parametric methods.

Mild, unavoidable deviations from circular-symmetry of instrumental beams in current Cosmic Microwave Background (CMB) experiments now pose a significant challenge to deriving high precision inferences from the high sensitivity and resolution of CMB measurements. We present analytic results, verified by numerical simulations, that CMB maps of cosmological signal that respect underlying statistical isotropy (SI) symmetry, measured with an instrument that has mildly non-circular (NC) beam would, nevertheless, exhibit SI violation. Further, we show that appropriate observable measures constructed within the Bipolar spherical harmonic (BipoSH) representation of SI violation capture subtle NC-beam effects coupled with the scan strategy of the instrument. Accompanying their latest 7-year data release, the WMAP team published very high significance measurements of non-zero BipoSH spectra, A^{20}_{l l} and A^{20}_{l-2 l}, in the "W" and "V" band of the experiment. We present a strong case that the BipoSH measurement are primarily explained by the quadrupolar (m=2) component of the NC-beams, b_{l2}, of the respective channels. The fact that subtle levels of non-circularity, e.g., WMAP beams |b_{l2}|/b_{l0} < 0.01, lead to measurable BipoSH spectra points to the immense promise and potential of the BipoSH representation. The key result of this work is that using BipoSH measurements it is possible to estimate an equivalent single hit,'parallel transported' effective NC-beam that matches both the angular power spectrum and the non-zero BipoSH measurements of the observed maps. Hence, BipoSH analysis provides a very simple and effective characterization of CMB maps made with NC-beam. (Abridged), Comment: 23 pages, 9 figures, Significant update from previous version, results from simulations using actual WMAP beam and scan pattern included, Comments and suggestions are welcome

A number of studies of WMAP-7 have highlighted that the power at the low multipoles in CMB power spectrum are lower than their theoretically predicted values. Angular correlation between the orientations of these low multipoles have also been discovered. While these observations may have cosmological ramification, it is important to investigate possible observational artifacts that can mimic them. The CMB dipole which is almost 550 times higher than the quadrupole can get leaked to the higher multipoles due to the non-circular beam of the CMB experiment. In this paper an analytical method has been developed and simulations are carried out to study the effect of the non-circular beam on power leakage from the dipole. It has been shown that the small, but non-negligible power from the dipole can get transferred to the quadrupole and the higher multipoles due to the non-circular beam. Simulations have also been carried out for Planck scan strategy and comparative results between WMAP and Planck have been presented in the paper., Comment: 4 pages, 6 figures, Submitted to Proc. of the 7th International Conference on Gravitation and Cosmology (ICGC-2011), Goa, India. (Dec 14-19, 2011)