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Although theoretically expected to be statistically isotropic (SI), the observed cosmic microwave background (CMB) temperature and polarization field would exhibit SI violation due to various inevitable effects like weak lensing, Doppler boost, and practical limitations of observations like noncircular beam, masking, etc. However, the presence of any SI violation beyond these effects may lead to a discovery of inherent cosmic SI violation in the CMB temperature and 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 the CMB temperature field. The nSI Gaussian temperature field leads to nonzero 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 nonisotropic Gaussian sky (CoNIGS) to generate nSI realizations of the Gaussian CMB temperature field of Planck-like resolution with specific cases of SI violation. Realizations of nSI CMB temperature field are obtained for nonzero quadrupolar (L = 2) BipoSH measurements by WMAP, dipolar asymmetry (resembles L = 1 BipoSH coefficients) with a 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. [ABSTRACT FROM AUTHOR]

Constraining theoretical models, which are represented by a set of parameters, using observational data is an important exercise in cosmology. In Bayesian framework this is done by finding the probability distribution of parameters which best fits to the observational data using sampling based methods like Markov chain Monte Carlo (MCMC). It has been argued that MCMC may not be the best option in certain problems in which the target function (likelihood) poses local maxima or have very high dimensionality. Apart from this, there may be examples in which we are mainly interested to find the point in the parameter space at which the probability distribution has the largest value. In this situation the problem of parameter estimation becomes an optimization problem. In the present work we show that particle swarm optimization (PSO), which is an artificial intelligence inspired population based search procedure, can also be used for cosmological parameter estimation. Using PSO we were able to recover the best-fit A cold dark matter (LCDM) model parameters from the WMAP seven year data without using any prior guess value or any other property of the probability distribution of parameters like standard deviation, as is common in MCMC. We also report the results of an exercise in which we consider a binned primordial power spectrum (to increase the dimensionality of problem) and find that a power spectrum with features gives lower chi square than the standard power law. Since PSO does not sample the likelihood surface in a fair way, we follow a fitting procedure to find the spread of likelihood function around the best-fit point. [ABSTRACT FROM AUTHOR]

Measurement of the CMB bispectrum, or three-point correlation function, has now become one of the principle efforts in early-Universe cosmology. Here we show that there is an odd-parity component of the CMB bispectrum that has been hitherto unexplored. We argue that odd-parity temperature-polarization bispectra can arise, in principle, through weak lensing of the CMB by chiral gravitational waves or through cosmological birefringence, although the signals will be small even in the best-case scenarios. Measurement of these bispectra requires only modest modifications to the usual data-analysis algorithms. They may be useful as a consistency test in searches for the usual bispectrum and to search for surprises in the data. [ABSTRACT FROM AUTHOR]

The simplest models of inflation based on slow roll produce nearly scale invariant primordial power spectra (PPS). But there are also numerous models that predict radically broken scale invariant PPS. In particular, markedly cuspy dips in the PPS correspond to nulls where the perturbation amplitude, hence PPS, goes through a zero at a specific wave number. Near this wave number, the true quantum nature of the generation mechanism of the primordial fluctuations may be revealed. Naively these features may appear to arise from fine-tuned initial conditions. However, we show that this behavior arises under fairly generic set of conditions involving super-Hubble scale evolution of perturbation modes during inflation. We illustrate this with the well-studied examples of punctuated inflation and the Starobinsky-break model. [ABSTRACT FROM AUTHOR]

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 P. A. R. Ade et al., arXiv:1303.5083 [Astron. Astrophys. (to be published)]; N. Aghanim et al., arXiv:1303.5087. We calculate the effect of our local motion with velocity (β ≡ |v|/c = 1.23 x 10~3) on the 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 β, the effect on the angular power spectra that correspond to the diagonal terms in the spherical harmonic space is at 0(β²). But nonzero off-diagonal terms at the linear order in β could provide a measurable signature of SI violation in the bipolar spherical harmonic (BipoSH) representation. We also calculate the measurability of β from polarization maps from experiments like Planck and PRISM. It is possible to measure β from the ideal, cosmic variance limited BipoSH spectra of EE, TE, BB, but not in EB and TB. With the instrumental noise and angular resolution of Planck, it is not possible to measure β with high statistical significance from BipoSH spectra of polarization. PRISM can measure β with high significance in both EE and TE BipoSH spectra, but not in BB, EB and TB BipoSH spectra. [ABSTRACT FROM AUTHOR]

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 entire data in the near future. In this paper, we provide model-independent forecasts for the TT, EE, and T E angular power spectra for the Planck mission using synthetic data based on the best-fit Lambda cold dark matter (ACDM) model. The nonparametric function estimation methodology we use here is based on the agnostic viewpoint of allowing the data to speak for themselves rather than letting the models decide what is inferred from the data. Our analysis indicates that the three Planck angular power spectra will be determined sufficiently well for 2 ≤l≲ lmax, where lmax = 2500(TT), 1377(EE), and 1727(TE) respectively. A key signature of reionization, namely, a bump at low values of I, is evident in our forecasts for the EE and T E power spectra. Nonparametric confidence bands in the phase shift (ɸm) versus acoustic scale (lA) plane, corresponding to the first eight peaks in the TT power spectrum, show a confluence region for 300 ≲ lA ≲ 305 which is in good agreement with the estimate lA = 300 based on the best-fit ACDM model. From our results, we expect that the final Planck data should lead to accurate model-independent estimates of CMB angular power spectra using our nonparametric regression formalism. [ABSTRACT FROM AUTHOR]

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 (GWs) 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 ß-mode power spectra measurements can be used to place interesting constraints on GW energy densities. [ABSTRACT FROM AUTHOR]

Constraints on the main cosmological parameters using cosmic microwave background (CMB) or large scale structure data are usually based on the 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 a direct reconstruction of the PPS for any point in the cosmological parameter space using the 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 the 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 a 4σ 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 the baryonic and matter density and a lower value of the 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 a free form of the PPS have an overlap at 1σ confidence level with the estimated values assuming the power-law form of PPS. [ABSTRACT FROM AUTHOR]

Gaussianity of temperature fluctuations in the Cosmic Microwave Background (CMB) implies that the statistical properties of the temperature field can be completely characterized by its two-point correlation function. The two-point correlation function can be expanded in full generality in the Bipolar Spherical Harmonic (BipoSH) basis. Looking for significant deviations from zero for BipoSH coefficients derived from observed CMB maps forms the basis of the strategy used to detect isotropy violation. In order to quantify "significant deviation" we need to understand the distributions of these coefficients. We analytically evaluate the moments and the distribution of the coefficients of expansion (ALMl1,l2) using the characteristic function approach. We show that for BipoSH coefficients with M ≠ 0 an analytical form for the moments up to any arbitrary order can be derived. For the remaining BipoSH coefficients with M i2 0, the moments derived using the characteristic function approach need to be supplemented with a correction term. The correction term is found to be important particularly at low multipoles. We provide a general prescription for calculating these corrections, however we restrict the explicit calculations only up to kurtosis. We confirm our results with measurements of BipoSH coefficients on numerically simulated statistically isotropic CMB maps. [ABSTRACT FROM AUTHOR]

Amongst the multitude of inflationary models currently available, models that lead to features in the primordial scalar spectrum are drawing increasing attention, since certain features have been found to provide a better fit to the cosmic microwave background data than the conventional, nearly scale invariant, primordial spectrum. In this work, we carry out a complete numerical analysis of two models that lead to oscillations over all scales in the scalar power spectrum. We consider the model described by a quadratic potential which is superposed by a sinusoidal modulation and the recently popular axion monodromy model. Since the oscillations continue even on to arc minute scales, in addition to the WMAP data, we also compare the models with the small scale data from ACT. Though, both the models, broadly, result in oscillations in the spectrum; interestingly, we find that, while the monodromy model leads to a considerably better fit to the data in comparison to the standard power law spectrum, the quadratic potential superposed with a sinusoidal modulation does not improve the fit to a similar extent. We also carry out forecasting of the parameters using simulated Planck data for both the models. We show that the Planck mock data performs better in constraining the model parameters as compared to the presently available cosmic microwave background datasets. [ABSTRACT FROM AUTHOR]