A Small-Scale Modification to the Lensing Kernel

Calculations of the Cosmic Microwave Background lensing power implemented into the standard cosmological codes such as CAMB and CLASS usually treat the surface of last scatter as an infinitely thin screen. However, since the CMB anisotropies are smoothed out on scales smaller than the diffusion length due to the effect of Silk damping, the photons which carry information about the small-scale density distribution come from slightly earlier times than the standard recombination time. The dominant effect is the scale dependence of the mean redshift associated with the fluctuations during recombination. We find that fluctuations at $k = 0.01 {\rm \ Mpc^{-1}}$ come from a characteristic redshift of $z \approx 1090$, while fluctuations at $k = 0.3 {\rm \ Mpc^{-1}}$ come from a characteristic redshift of $z \approx 1130$. We then estimate the corrections to the lensing kernel and the related power spectra due to this effect. We conclude that neglecting it would result in a deviation from the true value of the lensing kernel at the half percent level at small CMB scales. For an all-sky, noise-free experiment, this corresponds to a $\sim 0.1 \sigma$ shift in the observed temperature power spectrum on small scales ($2500 \lesssim l \lesssim 4000$).Comment: 5 pages, 5 figure

Neutrino masses and beyond-Λ\LambdaCDM cosmology with LSST and future CMB experiments

Cosmological measurements over the next decade will enable us to shed light on the content and evolution of the Universe. Complementary measurements of the Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillations are expected to allow an indirect determination of the sum of neutrino masses, within the framework of the flat $\Lambda$CDM model. However, possible deviations from $\Lambda$CDM such as a non-zero cosmological curvature or a dark energy equation of state with $w\neq -1$ would leave similar imprints on the expansion rate of the Universe and clustering of matter. We show how future CMB measurements can be combined with late-time measurements of galaxy clustering and cosmic shear from the Large Synoptic Survey Telescope to alleviate this degeneracy. Together, they are projected to reduce the uncertainty on the neutrino mass sum to 30 meV within this more general cosmological model. Achieving a 3$\sigma$ measurement of the minimal 60 meV mass (or 4$\sigma$ assuming $w=-1$) will require a five-fold improved measurement of the optical depth to reionization, obtainable through a large-scale CMB polarization measurement.Comment: 10 pages, 6 figures; v2, updated to PRD version, references adde

Simulated forecasts for primordial B-mode searches in ground-based experiments

Detecting the imprint of inflationary gravitational waves on the $B$-mode polarization of the Cosmic Microwave Background (CMB) is one of the main science cases for current and next-generation CMB experiments. In this work we explore some of the challenges that ground-based facilities will have to face in order to carry out this measurement in the presence of Galactic foregrounds and correlated atmospheric noise. We present forecasts for Stage-3 (S3) and planned Stage-4 (S4) experiments based on the analysis of simulated sky maps using a map-based Bayesian foreground cleaning method. Our results thus consistently propagate the uncertainties on foreground parameters such as spatially-varying spectral indices, as well as the bias on the measured tensor-to-scalar ratio $r$ caused by an incorrect modelling of the foregrounds. We find that S3 and S4-like experiments should be able to put constraints on $r$ of the order $\sigma(r)=(0.5-1.0)\times10^{-2}$ and $\sigma(r)=(0.5-1.0)\times10^{-3}$ respectively, assuming instrumental systematic effects are under control. We further study deviations from the fiducial foreground model, finding that, while the effects of a second polarized dust component would be minimal on both S3 and S4, a 2\% polarized anomalous dust emission (AME) component would be clearly detectable by Stage-4 experiments.Comment: 19 pages, 11 figure

Contamination of early-type galaxy alignments to galaxy lensing-CMB lensing cross-correlation

Galaxy shapes are subject to distortions due to the tidal field of the Universe. The cross-correlation of galaxy lensing with the lensing of the Cosmic Microwave Background (CMB) cannot easily be separated from the cross-correlation of galaxy intrinsic shapes with CMB lensing. Previous work suggested that the intrinsic alignment contamination can be $15\%$ of this cross-spectrum for the CFHT Stripe 82 (CS82) and Atacama Cosmology Telescope surveys. Here we re-examine these estimates using up-to-date observational constraints of intrinsic alignments at a redshift more similar to that of CS82 galaxies. We find a $\approx$ $10\%$ contamination of the cross-spectrum from red galaxies, with $\approx$ $3\%$ uncertainty due to uncertainties in the redshift distribution of source galaxies and the modelling of the spectral energy distribution. Blue galaxies are consistent with being unaligned, but could contaminate the cross-spectrum by an additional $9.5\%$ within current $95\%$ confidence levels. While our fiducial estimate of alignment contamination is similar to previous work, our work suggests that the relevance of alignments for CMB lensing-galaxy lensing cross-correlation remains largely unconstrained. Little information is currently available about alignments at $z>1.2$. We consider the upper limiting case where all $z>1.2$ galaxies are aligned with the same strength as low redshift luminous red galaxies, finding as much as $\approx$ $60\%$ contamination.Comment: 11 pages, 3 figures, MNRAS submitte

Towards a cosmological neutrino mass detection

Future cosmological measurements should enable the sum of neutrino masses to be determined indirectly through their effects on the expansion rate of the Universe and the clustering of matter. We consider prospects for the gravitationally lensed Cosmic Microwave Background anisotropies and Baryon Acoustic Oscillations in the galaxy distribution, examining how the projected uncertainty of $\approx15$ meV on the neutrino mass sum (a 4$\sigma$ detection of the minimal mass) might be reached over the next decade. The current 1$\sigma$ uncertainty of $\approx 103$ meV (Planck-2015+BAO-15) will be improved by upcoming 'Stage-3' CMB experiments (S3+BAO-15: 44 meV), then upcoming BAO measurements (S3+DESI: 22 meV), and planned next-generation 'Stage 4' CMB experiments (S4+DESI: 15-19 meV, depending on angular range). An improved optical depth measurement is important: the projected neutrino mass uncertainty increases to $26$ meV if S4 is limited to $\ell>20$ and combined with current large-scale polarization data. Looking beyond $\Lambda$CDM, including curvature uncertainty increases the forecast mass error by $\approx$ 50% for S4+DESI, and more than doubles the error with a two-parameter dark energy equation of state. Complementary low-redshift probes including galaxy lensing will play a role in distinguishing between massive neutrinos and a departure from a $w=-1$, flat geometry.Comment: Submitted to PRD. 15 pages, 10 figure

Lensing Simulation and Power Spectrum Estimation for High Resolution CMB Polarization Maps

We present efficient algorithms for CMB lensing simulation and power spectrum es- timation for flat-sky CMB polarization maps. We build a pure B-mode estimator to remedy E to B leakage due to partial sky coverage. We show that our estimators are unbiased, and consistent with the projected errors. We demonstrate our algorithm using simulated observations of small sky patches with realistic noise and weights for upcoming CMB polarization experiments.Comment: 11 pages, 6 figure

Constraining Isocurvature Initial Conditions with WMAP 3-year data

We present constraints on the presence of isocurvature modes from the temperature and polarization CMB spectrum data from the WMAP satellite alone, and in combination with other datasets including SDSS galaxy survey and SNLS supernovae. We find that the inclusion of polarization data allows the WMAP data alone, as well as in combination with complementary observations, to place improved limits on the contribution of CDM and neutrino density isocurvature components individually. With general correlations, the upper limits on these sub-dominant isocurvature components are reduced to ~60% of the first year WMAP results, with specific limits depending on the type of fluctuations. If multiple isocurvature components are allowed, however, we find that the data still allow a majority of the initial power to come from isocurvature modes. As well as providing general constraints we also consider their interpretation in light of specific theoretical models like the curvaton and double inflation.Comment: 8 pages, 7 figures. Revised Sec 4 and Figs 3-4 post-publication to correct an error for models with varying isocurvature spectral inde

Large-Scale Polarized Foreground Component Separation for Planck

We use Bayesian component estimation methods to examine the prospects for large-scale polarized map and cosmological parameter estimation with simulated Planck data assuming simplified white noise properties. The sky signal is parametrized as the sum of the CMB, synchrotron emission, and thermal dust emission. The synchrotron and dust components are modelled as power-laws, with a spatially varying spectral index for synchrotron and a uniform index for dust. Using the Gibbs sampling technique, we estimate the linear polarisation Q and U posterior amplitudes of the CMB, synchrotron and dust maps as well as the two spectral indices in ~4 degree pixels. We use the recovered CMB map and its covariance in an exact pixel likelihood algorithm to estimate the optical depth to reionization tau, the tensor-to-scalar ratio r, and to construct conditional likelihood slices for the EE and BB spectra. Given our foreground model, we find sigma(tau)~0.004 for tau=0.1, sigma(r)~0.03 for a model with r=0.1, and a 95% upper limit of r<0.02 for r=0.0.Comment: 15 pages, 12 figures, submitted to MNRA