The full squeezed CMB bispectrum from inflation

The small-scale CMB temperature we observe on the sky is modulated by perturbations that were super-horizon at recombination, giving differential focussing and lensing that generate a non-zero bispectrum even for single-field inflation where local physics is identical. Understanding this signal is important for primordial non-Gaussianity studies and also parameter constraints from the CMB lensing bispectrum signal. Because of cancellations individual effects can appear larger or smaller than they are in total, so a full analysis may be required to avoid biases. I relate angular scales on the sky to physical scales at recombination using the optical equations, and give full-sky results for the large-scale adiabatic temperature bispectrum from Ricci focussing (expansion of the ray bundle), Weyl lensing (convergence and shear), and temperature redshift modulations of small-scale power. The delta N expansion of the beam is described by the constant temperature 3-curvature, and gives a nearly-observable version of the consistency relation prediction from single-field inflation. I give approximate arguments to quantify the likely importance of dynamical effects, and argue that they can be neglected for modulation scales l <~ 100, which is sufficient for lensing studies and also allows robust tests of local primordial non-Gaussianity using only the large-scale modulation modes. For accurate numerical results early and late-time ISW effects must be accounted for, though I confirm that the late-time non-linear Rees-Sciama contribution is negligible compared to other more important complications. The total corresponds to f_NL ~ 7 for Planck-like temperature constraints and f_NL ~ 11 for cosmic-variance limited data to lmax=2000. Temperature lensing bispectrum estimates are affected at the 0.2 sigma level by Ricci focussing, and up to 0.5 sigma with polarization.Comment: 12 pages, 5 figures; typos corrected, minor edit

Estimators for CMB Statistical Anisotropy

We use quadratic maximum-likelihood (QML) estimators to constrain models with Gaussian but statistically anisotropic Cosmic Microwave Background (CMB) fluctuations, using CMB maps with realistic sky-coverage and instrumental noise. This approach is optimal when the anisotropy is small, or when checking for consistency with isotropy. We demonstrate the power of the QML approach by applying it to the WMAP data to constrain several models which modulate the observed CMB fluctuations to produce a statistically anisotropic sky. We first constrain an empirically motivated spatial modulation of the observed CMB fluctuations, reproducing marginal evidence for a dipolar modulation pattern with amplitude 7% at L < 60, but demonstrate that the effect decreases at higher multipoles and is 1% at L~500. We also look for evidence of a direction-dependent primordial power spectrum, finding a very statistically significant quadrupole signal nearly aligned with the ecliptic plane; however we argue this anisotropy is largely contaminated by observational systematics. Finally, we constrain the anisotropy due to a spatial modulation of adiabatic and isocurvature primordial perturbations, and discuss the close relationship between anisotropy and non-Gaussianity estimators.Comment: add missed ref. to Gordon et. al. 200

Accuracy of cosmological parameters using the baryon acoustic scale

Percent-level measurements of the comoving baryon acoustic scale standard ruler can be used to break degeneracies in parameter constraints from the CMB alone. The sound horizon at the epoch of baryon drag is often used as a proxy for the scale of the peak in the matter density correlation function, and can conveniently be calculated quickly for different cosmological models. However, the measurements are not directly constraining this scale, but rather a measurement of the full correlation function, which depends on the detailed evolution through decoupling. We assess the level of reliability of parameter constraints based on a simple approximation of the acoustic scale compared to a more direct determination from the full numerical two-point correlation function. Using a five-parameter fitting technique similar to recent BAO data analyses, we find that for standard _CDM models and extensions with massive neutrinos and additional relativistic degrees of freedom, the approximation is at better than 0:15% for most parameter combinations varying over reasonable ranges

Non-linear Redshift-Space Power Spectra

Distances in cosmology are usually inferred from observed redshifts - an estimate that is dependent on the local peculiar motion - giving a distorted view of the three dimensional structure and affecting basic observables such as the correlation function and power spectrum. We calculate the full non-linear redshift-space power spectrum for Gaussian fields, giving results for both the standard flat sky approximation and the directly-observable angular correlation function and angular power spectrum. Coupling between large and small scale modes boosts the power on small scales when the perturbations are small. On larger scales power is slightly suppressed by the velocities perturbations on smaller scales. The analysis is general, but we comment specifically on the implications for future high-redshift observations, and show that the non-linear spectrum has significantly more complicated angular structure than in linear theory. We comment on the implications for using the angular structure to separate cosmological and astrophysical components of 21 cm observations.Comment: 22 pages, 6 figures, changed to version accepted in Physics Review

Crossing the Phantom Divide with Parameterized Post-Friedmann Dark Energy

Dark energy models with a single scalar field cannot cross the equation of state divide set by a cosmological constant. More general models that allow crossing require additional degrees of freedom to ensure gravitational stability. We show that a parameterized post-Friedmann description of cosmic acceleration provides a simple but accurate description of multiple scalar field crossing models. Moreover the prescription provides a well controlled approximation for a wide range of "smooth" dark energy models. It conserves energy and momentum and is exact in the metric evolution on scales well above and below the transition scale to relative smoothness. Standard linear perturbation tools have been altered to include this description and made publicly available for studies of the dark energy involving cosmological structure out to the horizon scale.Comment: 4 pages, 2 figures, code available at http://camb.info/ppf, minor revisions reflect PRD published versio

CMB lensing reconstruction using cut sky polarization maps and pure B modes

Detailed measurements of the CMB lensing signal are an important scientific goal of ongoing groundbased CMB polarization experiments, which are mapping the CMB at high resolution over small patches of the sky. In this work we simulate CMB polarization lensing reconstruction for the EE and EB quadratic estimators with current-generation noise levels and resolution, and show that without boundary effects the known and expected zeroth and first order Nð0Þ and Nð1Þ biases provide an adequate model for nonsignal contributions to the lensing power spectrum estimators. Small sky areas present a number of additional challenges for polarization lensing reconstruction, including leakage of E modes into B modes. We show how simple windowed estimators using filtered pure B modes can greatly reduce the mask-induced meanfield lensing signal and reduce variance in the estimators. This provides a simple method (used with recent observations) that gives an alternative to more optimal but expensive inverse-variance filtering