Search

Millimeter-wave refracting telescopes targeting the degree-scale structure of the cosmic microwave background (CMB) have recently grown to diffraction-limited apertures of over 0.5 meters. These instruments are entirely housed in vacuum cryostats to support their sub-kelvin bolometric detectors and to minimize radiative loading from thermal emission due to absorption loss in their transmissive optical elements. The large vacuum window is the only optical element in the system at ambient temperature, and therefore minimizing loss in the window is crucial for maximizing detector sensitivity. This motivates the use of low-loss polymer materials and a window as thin as practicable. However, the window must simultaneously meet the requirement to keep sufficient vacuum, and therefore must limit gas permeation and remain mechanically robust against catastrophic failure under pressure. We report on the development of extremely thin composite polyethylene window technology that meets these goals. Two windows have been deployed for two full observing seasons on the BICEP3 and BA150 CMB telescopes at the South Pole. On BICEP3, the window has demonstrated a 6% improvement in detector sensitivity., Comment: 20 pages, 12 figures, 4 tables

We use a custom-made calibrator to measure individual detectors' polarization angles of BICEP3, a small aperture telescope observing the cosmic microwave background (CMB) at 95GHz from the South Pole. We describe our calibration strategy and the statistical and systematic uncertainties associated with the measurement. We reach an unprecedented precision for such measurement on a CMB experiment, with a repeatability for each detector pair of $0.02\deg$. We show that the relative angles measured using this method are in excellent agreement with those extracted from CMB data. Because the absolute measurement is currently limited by a systematic uncertainty, we do not derive cosmic birefringence constraints from BICEP3 data in this work. Rather, we forecast the sensitivity of BICEP3 sky maps for such analysis. We investigate the relative contributions of instrument noise, lensing, and dust, as well as astrophysical and instrumental systematics. We also explore the constraining power of different angle estimators, depending on analysis choices. We establish that the BICEP3 2-year dataset (2017--2018) has an on-sky sensitivity to the cosmic birefringence angle of $\sigma = 0.078\deg$, which could be improved to $\sigma = 0.055\deg$ by adding all of the existing BICEP3 data (through 2023). Furthermore, we emphasize the possibility of using the BICEP3 sky patch as a polarization calibration source for CMB experiments, which with the present data could reach a precision of $0.035\deg$. Finally, in the context of inflation searches, we investigate the impact of detector-to-detector variations in polarization angles as they may bias the tensor-to-scalar ratio r. We show that while the effect is expected to remain subdominant to other sources of systematic uncertainty, it can be reliably calibrated using polarization angle measurements such as the ones we present in this paper., Comment: 29 Pages, 17 Figures, 6 Tables, as submitted to PRD. Visit bicepkeck.org for figure pdfs/pngs

Measurements of B-mode polarization in the CMB sourced from primordial gravitational waves would provide information on the energy scale of inflation and its potential form. To achieve these goals, one must carefully characterize the Galactic foregrounds, which can be distinguished from the CMB by conducting measurements at multiple frequencies. BICEP Array is the latest-generation multi-frequency instrument of the BICEP/Keck program, which specifically targets degree-scale primordial B-modes in the CMB. In its final configuration, this telescope will consist of four small-aperture receivers, spanning frequency bands from 30 to 270 GHz. The 220/270 GHz receiver designed to characterize Galactic dust is currently undergoing commissioning at Stanford University and is scheduled to deploy to the South Pole during the 2024--2025 austral summer. Here, we will provide an overview of this high-frequency receiver and discuss the integration status and test results as it is being commissioned.

The BICEP/$\textit{Keck}$ (BK) series of cosmic microwave background (CMB) polarization experiments has, over the past decade and a half, produced a series of field-leading constraints on cosmic inflation via measurements of the "B-mode" polarization of the CMB. Primordial B modes are directly tied to the amplitude of primordial gravitational waves (PGW), their strength parameterized by the tensor-to-scalar ratio, $r$, and thus the energy scale of inflation. Having set the most sensitive constraints to-date on $r$, $\sigma(r)=0.009$ ($r_{0.05}<0.036, 95\%$ C.L.) using data through the 2018 observing season ("BK18"), the BICEP/$\textit{Keck}$ program has continued to improve its dataset in the years since. We give a brief overview of the BK program and the "BK18" result before discussing the program's ongoing efforts, including the deployment and performance of the $\textit{Keck Array}$'s successor instrument, BICEP Array, improvements to data processing and internal consistency testing, new techniques such as delensing, and how those will ultimately serve to allow BK reach $\sigma(r) \lesssim 0.003$ using data through the 2027 observing season., Comment: 9 pages, 5 figures. Contribution to the 2024 Cosmology session of the 58th Rencontres de Moriond

Time-Division Multiplexing is the readout architecture of choice for many ground and space experiments, as it is a very mature technology with proven outstanding low-frequency noise stability, which represents a central challenge in multiplexing. Once fully populated, each of the two BICEP Array high frequency receivers, observing at 150GHz and 220/270GHz, will have 7776 TES detectors tiled on the focal plane. The constraints set by these two receivers required a redesign of the warm readout electronics. The new version of the standard Multi Channel Electronics, developed and built at the University of British Columbia, is presented here for the first time. BICEP Array operates Time Division Multiplexing readout technology to the limits of its capabilities in terms of multiplexing rate, noise and crosstalk, and applies them in rigorously demanding scientific application requiring extreme noise performance and systematic error control. Future experiments like CMB-S4 plan to use TES bolometers with Time Division/SQUID-based readout for an even larger number of detectors., Comment: 10 pages, 7 figures, Submitted to Journal of Low Temperature Physics

We present estimates of line-of-sight distortion fields derived from the 95 GHz and 150 GHz data taken by BICEP2, BICEP3, and Keck Array up to the 2018 observing season, leading to cosmological constraints and a study of instrumental and astrophysical systematics. Cosmological constraints are derived from three of the distortion fields concerning gravitational lensing from large-scale structure, polarization rotation from magnetic fields or an axion-like field, and the screening effect of patchy reionization. We measure an amplitude of the lensing power spectrum $A_L^{\phi\phi}=0.95 \pm 0.20$. We constrain polarization rotation, expressed as the coupling constant of a Chern-Simons electromagnetic term $g_{a\gamma} \leq 2.6 \times 10^{-2}/H_I$, where $H_I$ is the inflationary Hubble parameter, and an amplitude of primordial magnetic fields smoothed over 1 Mpc $B_{1\text{Mpc}} \leq 6.6 \;\text{nG}$ at 95 GHz. We constrain the root mean square of optical-depth fluctuations in a simple "crinkly surface" model of patchy reionization, finding $A^\tau<0.19$ ($2\sigma$) for the coherence scale of $L_c=100$. We show that all of the distortion fields of the 95 GHz and 150 GHz polarization maps are consistent with simulations including lensed-$\Lambda$CDM, dust, and noise, with no evidence for instrumental systematics. In some cases, the EB and TB quadratic estimators presented here are more sensitive than our previous map-based null tests at identifying and rejecting spurious B-modes that might arise from instrumental effects. Finally, we verify that the standard deprojection filtering in the BICEP/Keck data processing is effective at removing temperature to polarization leakage., Comment: 34 pages, 19 figures, accepted for publication in The Astrophysical Journal

We characterize Galactic dust filaments by correlating BICEP/Keck and Planck data with polarization templates based on neutral hydrogen (H I) observations. Dust polarization is important for both our understanding of astrophysical processes in the interstellar medium (ISM) and the search for primordial gravitational waves in the cosmic microwave background (CMB). In the diffuse ISM, H I is strongly correlated with the dust and partly organized into filaments that are aligned with the local magnetic field. We analyze the deep BICEP/Keck data at 95, 150, and 220 GHz, over the low-column-density region of sky where BICEP/Keck has set the best limits on primordial gravitational waves. We separate the H I emission into distinct velocity components and detect dust polarization correlated with the local Galactic H I but not with the H I associated with Magellanic Stream I. We present a robust, multifrequency detection of polarized dust emission correlated with the filamentary H I morphology template down to 95 GHz. For assessing its utility for foreground cleaning, we report that the H I morphology template correlates in B modes at a $\sim$10-65$\%$ level over the multipole range $20 < \ell < 200$ with the BICEP/Keck maps, which contain contributions from dust, CMB, and noise components. We measure the spectral index of the filamentary dust component spectral energy distribution to be $\beta = 1.54 \pm 0.13$. We find no evidence for decorrelation in this region between the filaments and the rest of the dust field or from the inclusion of dust associated with the intermediate velocity H I. Finally, we explore the morphological parameter space in the H I-based filamentary model., Comment: 27 pages, 12 figures

Observations of the Cosmic Microwave Background rely on cryogenic instrumentation with cold detectors, readout, and optics providing the low noise performance and instrumental stability required to make more sensitive measurements. It is therefore critical to optimize all aspects of the cryogenic design to achieve the necessary performance, with low temperature components and acceptable system cooling requirements. In particular, we will focus on our use of thermal filters and cold optics, which reduce the thermal load passed along to the cryogenic stages. To test their performance, we have made a series of in situ measurements while integrating the third receiver for the BICEP Array telescope. In addition to characterizing the behavior of this receiver, these measurements continue to refine the models that are being used to inform design choices being made for future instruments., Comment: 9 pages, 8 figures, Proceedings of SPIE 2022

Constraining the Galactic foregrounds with multi-frequency Cosmic Microwave Background (CMB) observations is an essential step towards ultimately reaching the sensitivity to measure primordial gravitational waves (PGWs), the sign of inflation after the Big-Bang that would be imprinted on the CMB. The BICEP Array telescope is a set of multi-frequency cameras designed to constrain the energy scale of inflation through CMB B-mode searches while also controlling the polarized galactic foregrounds. The lowest frequency BICEP Array receiver (BA1) has been observing from the South Pole since 2020 and provides 30 GHz and 40 GHz data to characterize the Galactic synchrotron in our CMB maps. In this paper, we present the design of the BA1 detectors and the full optical characterization of the camera including the on-sky performance at the South Pole. The paper also introduces the design challenges during the first observing season including the effect of out-of-band photons on detectors performance. It also describes the tests done to diagnose that effect and the new upgrade to minimize these photons, as well as installing more dichroic detectors during the 2022 deployment season to improve the BA1 sensitivity. We finally report background noise measurements of the detectors with the goal of having photon noise dominated detectors in both optical channels. BA1 achieves an improvement in mapping speed compared to the previous deployment season., Comment: Proceedings of SPIE Astronomical Telescopes + Instrumentation 2022 (AS22)

The BICEP3 Polarimeter is a small aperture, refracting telescope, dedicated to the observation of the Cosmic Microwave Background (CMB) at 95GHz. It is designed to target degree angular scale polarization patterns, in particular the very-much-sought-after primordial B-mode signal, which is a unique signature of cosmic inflation. The polarized signal from the sky is reconstructed by differencing co-localized, orthogonally polarized superconducting Transition Edge Sensor (TES) bolometers. In this work, we present absolute measurements of the polarization response of the detectors for more than $\sim 800$ functioning detector pairs of the BICEP3 experiment, out of a total of $\sim 1000$. We use a specifically designed Rotating Polarized Source (RPS) to measure the polarization response at multiple source and telescope boresight rotation angles, to fully map the response over 360 degrees. We present here polarization properties extracted from on-site calibration data taken in January 2022. A similar calibration campaign was performed in 2018, but we found that our constraint was dominated by systematics on the level of $\sim0.5^\circ$. After a number of improvements to the calibration set-up, we are now able to report a significantly lower level of systematic contamination. In the future, such precise measurements will be used to constrain physics beyond the standard cosmological model, namely cosmic birefringence., Comment: Submitted to: SPIE Astronomical Telescopes + Instrumentation (AS22)

For the past decade, the BICEP/Keck collaboration has been operating a series of telescopes at the Amundsen-Scott South Pole Station measuring degree-scale $B$-mode polarization imprinted in the Cosmic Microwave Background (CMB) by primordial gravitational waves (PGWs). These telescopes are compact refracting polarimeters mapping about 2% of the sky, observing at a broad range of frequencies to account for the polarized foreground from Galactic synchrotron and thermal dust emission. Our latest publication "BK18" utilizes the data collected up to the 2018 observing season, in conjunction with the publicly available WMAP and Planck data, to constrain the tensor-to-scalar ratio $r$. It particularly includes (1) the 3-year BICEP3 data which is the current deepest CMB polarization map at the foreground-minimum 95 GHz; and (2) the Keck 220 GHz map with a higher signal-to-noise ratio on the dust foreground than the Planck 353 GHz map. We fit the auto- and cross-spectra of these maps to a multicomponent likelihood model ($\Lambda$CDM+dust+synchrotron+noise+$r$) and find it to be an adequate description of the data at the current noise level. The likelihood analysis yields $\sigma(r)=0.009$. The inference of $r$ from our baseline model is tightened to $r_{0.05}=0.014^{+0.010}_{-0.011}$ and $r_{0.05}<0.036$ at 95% confidence, meaning that the BICEP/Keck $B$-mode data is the most powerful existing dataset for the constraint of PGWs. The up-coming BICEP Array telescope is projected to reach $\sigma(r) \lesssim 0.003$ using data up to 2027., Comment: 8 pages, 6 figures, contribution to the 2022 Cosmology session of the 56th Rencontres de Moriond

The BICEP/Keck Collaboration is currently leading the quest to the highest sensitivity measurements of the polarized CMB anisotropies on degree scale with a series of cryogenic telescopes, of which BICEP Array is the latest Stage-3 upgrade with a total of $\sim32,000$ detectors. The instrument comprises 4 receivers spanning 30 to 270 GHz, with the low-frequency 30/40 GHz deployed to the South Pole Station in late 2019. The full complement of receivers is forecast to set the most stringent constraints on the tensor to scalar ratio $r$. Building on these advances, the overarching small-aperture telescope concept is already being used as the reference for further Stage-4 experiment design. In this paper I will present the development of the BICEP Array 150 GHz detector module and its fabrication requirements, with highlights on the high-density time division multiplexing (TDM) design of the cryogenic circuit boards. The low-impedance wiring required between the detectors and the first-stage SQUID amplifiers is crucial to maintain a stiff voltage bias on the detectors. A novel multi-layer FR4 Printed Circuit Board (PCB) with superconducting traces, capable of reading out up to 648 detectors, is presented along with its validation tests. I will also describe an ultra-high density TDM detector module we developed for a CMB-S4-like experiment that allows up to 1,920 detectors to be read out. TDM has been chosen as the detector readout technology for the Cosmic Microwave Background Stage-4 (CMB-S4) experiment based on its proven low-noise performance, predictable costs and overall maturity of the architecture. The heritage for TDM is rooted in mm- and submm-wave experiments dating back 20 years and has since evolved to support a multiplexing factor of 64x in Stage-3 experiments., Comment: 9 pages, 5 figure, Proceeding of LTD19 submitted to Journal of Low Temperature Physics

We present results from an analysis of all data taken by the BICEP2, Keck Array and BICEP3 CMB polarization experiments up to and including the 2018 observing season. We add additional Keck Array observations at 220 GHz and BICEP3 observations at 95 GHz to the previous 95/150/220 GHz data set. The $Q/U$ maps now reach depths of 2.8, 2.8 and 8.8 $\mu{\mathrm K}_{cmb}$ arcmin at 95, 150 and 220 GHz respectively over an effective area of $\approx 600$ square degrees at 95 GHz and $\approx 400$ square degrees at 150 & 220 GHz. The 220 GHz maps now achieve a signal-to-noise on polarized dust emission exceeding that of Planck at 353 GHz. We take auto- and cross-spectra between these maps and publicly available WMAP and Planck maps at frequencies from 23 to 353 GHz and evaluate the joint likelihood of the spectra versus a multicomponent model of lensed-$\Lambda$CDM+$r$+dust+synchrotron+noise. The foreground model has seven parameters, and no longer requires a prior on the frequency spectral index of the dust emission taken from measurements on other regions of the sky. This model is an adequate description of the data at the current noise levels. The likelihood analysis yields the constraint $r_{0.05}<0.036$ at 95% confidence. Running maximum likelihood search on simulations we obtain unbiased results and find that $\sigma(r)=0.009$. These are the strongest constraints to date on primordial gravitational waves., Comment: 22 pages, 24 figures, as published in PRL, data and figures available for download at http://bicepkeck.org

We report on the design and performance of the BICEP3 instrument and its first three-year data set collected from 2016 to 2018. BICEP3 is a 52cm aperture, refracting telescope designed to observe the polarization of the cosmic microwave background (CMB) on degree angular scales at 95GHz. It started science observation at the South Pole in 2016 with 2400 antenna-coupled transition-edge sensor (TES) bolometers. The receiver first demonstrated new technologies such as large-diameter alumina optics, Zotefoam infrared filters, and flux-activated SQUIDs, allowing $\sim 10\times$ higher optical throughput compared to the Keck design. BICEP3 achieved instrument noise-equivalent temperatures of 9.2, 6.8 and 7.1$\mu\text{K}_{\text{CMB}}\sqrt{\text{s}}$ and reached Stokes $Q$ and $U$ map depths of 5.9, 4.4 and 4.4$\mu$K-arcmin in 2016, 2017 and 2018, respectively. The combined three-year data set achieved a polarization map depth of 2.8$\mu$K-arcmin over an effective area of 585 square degrees, which is the deepest CMB polarization map made to date at 95GHz., Comment: 35 pages, 35 figures, as submitted to ApJ, data and figures available for download at http://bicepkeck.org

We present an improved search for axion-like polarization oscillations in the cosmic microwave background (CMB) with observations from the Keck Array. An all-sky, temporally sinusoidal rotation of CMB polarization, equivalent to a time-variable cosmic birefringence, is an observable manifestation of a local axion field and potentially allows a CMB polarimeter to detect axion-like dark matter directly. We describe improvements to the method presented in previous work, and we demonstrate the updated method with an expanded dataset consisting of the 2012-2015 observing seasons. We set limits on the axion-photon coupling constant for mass $m$ in the range $10^{-23}$-$10^{-18}~\mathrm{eV}$, which corresponds to oscillation periods on the order of hours to years. Our results are consistent with the background model. For periods between $1$ and $30~\mathrm{d}$ ($1.6 \times 10^{-21} \leq m \leq 4.8 \times 10^{-20}~\mathrm{eV}$), the $95\%$-confidence upper limits on rotation amplitude are approximately constant with a median of $0.27^\circ$, which constrains the axion-photon coupling constant to $g_{\phi\gamma} < (4.5 \times 10^{-12}~\mathrm{GeV}^{-1}) m/(10^{-21}~\mathrm{eV}$), if axion-like particles constitute all of the dark matter. More than half of the collected BICEP dataset has yet to be analyzed, and several current and future CMB polarimetry experiments can apply the methods presented here to achieve comparable or superior constraints. In the coming years, oscillation measurements can achieve the sensitivity to rule out unexplored regions of the axion parameter space., Comment: 14 pages, 3 figures

We report a measurement of the E-mode polarization power spectrum of the cosmic microwave background (CMB) using 150 GHz data taken from July 2014 to December 2016 with the POLARBEAR experiment. We reach an effective polarization map noise level of $32\,\mu\mathrm{K}$-$\mathrm{arcmin}$ across an observation area of 670 square degrees. We measure the EE power spectrum over the angular multipole range $500 \leq \ell <3000$, tracing the third to seventh acoustic peaks with high sensitivity. The statistical uncertainty on E-mode bandpowers is $\sim 2.3 \mu {\rm K}^2$ at $\ell \sim 1000$ with a systematic uncertainty of 0.5$\mu {\rm K}^2$. The data are consistent with the standard $\Lambda$CDM cosmological model with a probability-to-exceed of 0.38. We combine recent CMB E-mode measurements and make inferences about cosmological parameters in $\Lambda$CDM as well as in extensions to $\Lambda$CDM. Adding the ground-based CMB polarization measurements to the Planck dataset reduces the uncertainty on the Hubble constant by a factor of 1.2 to $H_0 = 67.20 \pm 0.57 {\rm km\,s^{-1} \,Mpc^{-1}}$. When allowing the number of relativistic species ($N_{eff}$) to vary, we find $N_{eff} = 2.94 \pm 0.16$, which is in good agreement with the standard value of 3.046. Instead allowing the primordial helium abundance ($Y_{He}$) to vary, the data favor $Y_{He} = 0.248 \pm 0.012$. This is very close to the expectation of 0.2467 from Big Bang Nucleosynthesis. When varying both $Y_{He}$ and $N_{eff}$, we find $N_{eff} = 2.70 \pm 0.26$ and $Y_{He} = 0.262 \pm 0.015$., Comment: 15 pages, 5 figures, submitted to ApJ

We present a measurement of the $B$-mode polarization power spectrum of the cosmic microwave background (CMB) using taken from July 2014 to December 2016 with the POLARBEAR experiment. The CMB power spectra are measured using observations at 150 GHz with an instantaneous array sensitivity of $\mathrm{NET}_\mathrm{array}=23\, \mu \mathrm{K} \sqrt{\mathrm{s}}$ on a 670 square degree patch of sky centered at (RA, Dec)=($+0^\mathrm{h}12^\mathrm{m}0^\mathrm{s},-59^\circ18^\prime$). A continuously rotating half-wave plate is used to modulate polarization and to suppress low-frequency noise. We achieve $32\,\mu\mathrm{K}$-$\mathrm{arcmin}$ effective polarization map noise with a knee in sensitivity of $\ell = 90$, where the inflationary gravitational wave signal is expected to peak. The measured $B$-mode power spectrum is consistent with a $\Lambda$CDM lensing and single dust component foreground model over a range of multipoles $50 \leq \ell \leq 600$. The data disfavor zero $C_\ell^{BB}$ at $2.2\sigma$ using this $\ell$ range of POLARBEAR data alone. We cross-correlate our data with Planck high frequency maps and find the low-$\ell$ $B$-mode power in the combined dataset to be consistent with thermal dust emission. We place an upper limit on the tensor-to-scalar ratio $r < 0.90$ at 95% confidence level after marginalizing over foregrounds.

Using only cosmic microwave background polarization data from the POLARBEAR experiment, we measure $B$-mode polarization delensing on subdegree scales at more than $5\sigma$ significance. We achieve a 14% $B$-mode power variance reduction, the highest to date for internal delensing, and improve this result to 2% by applying for the first time an iterative maximum a posteriori delensing method. Our analysis demonstrates the capability of internal delensing as a means of improving constraints on inflationary models, paving the way for the optimal analysis of next-generation primordial $B$-mode experiments., Comment: Matches version published in Physical Review Letters

We report a 4.8$\sigma$ measurement of the cross-correlation signal between the cosmic microwave background (CMB) lensing convergence reconstructed from measurements of the CMB polarization made by the POLARBEAR experiment and the infrared-selected galaxies of the Herschel-ATLAS survey. This is the first measurement of its kind. We infer a best-fit galaxy bias of $b = 5.76 \pm 1.25$, corresponding to a host halo mass of $\log_{10}(M_h/M_\odot) =13.5^{+0.2}_{-0.3}$ at an effective redshift of $z \sim 2$ from the cross-correlation power spectrum. Residual uncertainties in the redshift distribution of the sub-mm galaxies are subdominant with respect to the statistical precision. We perform a suite of systematic tests, finding that instrumental and astrophysical contaminations are small compared to the statistical error. This cross-correlation measurement only relies on CMB polarization information that, differently from CMB temperature maps, is less contaminated by galactic and extra-galactic foregrounds, providing a clearer view of the projected matter distribution. This result demonstrates the feasibility and robustness of this approach for future high-sensitivity CMB polarization experiments., Comment: 14 pages, 6 figures, updated to match published version on ApJ

Since the evidence for an accelerated universe and the gap of 70% in the total energy, collected by WMAP, search for alternatives for the general relativity is an important issue, for this theory is not suited for these new phenomena. A particular alternative is the Brans-Dicke theory which has being allowing inspiring results, for example, concerning k-essence type fields in 4 dimensions. However, this theory is almost unexplored in the context of the dimensional reduction of the theory in 3 dimensions. In this work, we address some problems in this dimensional reduction, namely, evaluation of the deceleration parameter of the universe described by the 3 dimensional Brans-Dicke with and without matter. In both cases, we see that it is not possible to consider the theory as a model of k-essence descrybing the dark energy, but it can be considered as descrybing the dark matter.

In presence of unstable dimension variability numerical solutions of chaotic systems are valid only for short periods of observation. For this reason, analytical results for systems that exhibit this phenomenon are needed. Aiming to go one step further in obtaining such results, we study the parametric evolution of unstable dimension variability in two coupled bungalow maps. Each of these maps presents intervals of linearity that define Markov partitions, which are recovered for the coupled system in the case of synchronization. Using such partitions we find exact results for the onset of unstable dimension variability and for contrast measure, which quantifies the intensity of the phenomenon in terms of the stability of the periodic orbits embedded in the synchronization subspace., Comment: 5 pages, 2 figures - to be submitted to Physical Review E - Brief Report

E. Verlinde obtained a generalized formula for the entropy of a conformal field theory. For this we consider a (n+1) dimensional closed radiation dominated FLWR in the context of the holographic principle. In this work we construct a extension of the Cardy-Verlinde formula to positive cosmological constant spaces (dS spaces) with arbitrary topology

We investigate the parametric evolution of riddled basins related to synchronization of chaos in two coupled piecewise-linear Lorenz maps. Riddling means that the basin of the synchronized attractor is shown to be riddled with holes belonging to another basin in an arbitrarily fine scale, which has serious consequences on the predictability of the final state for such a coupled system. We found that there are wide parameter intervals for which two piecewise-linear Lorenz maps exhibit riddled basins (globally or locally), which indicates that there are riddled basins in coupled Lorenz equations, as previously suggested by numerical experiments. The use of piecewise-linear maps makes it possible to prove rigorously the mathematical requirements for the existence of riddled basins., Comment: 22 pages (preprint format), 8 figures