Lensing effect on polarization in microwave background: extracting convergence power spectrum

Matter inhomogeneities along the line of sight deflect the cosmic microwave background (CMB) photons originating at the last scattering surface at redshift $z \sim 1100$. These distortions modify the pattern of CMB polarization. We identify specific combinations of Stokes $Q$ and $U$ parameters that correspond to spin 0,$\pm 2$ variables and can be used to reconstruct the projected matter density. We compute the expected signal to noise as a function of detector sensitivity and angular resolution. With Planck satellite the detection would be at a few $\sigma$ level. Several times better detector sensitivity would be needed to measure the projected dark matter power spectrum over a wider range of scales, which could provide an independent confirmation of the projected matter power spectrum as measured from other methods.Comment: 17 pages, 5 figures, accepted for publication in PR

Lensing of the CMB: Non Gaussian aspects

We study the generation of CMB anisotropies by gravitational lensing on small angular scales. We show these fluctuations are not Gaussian. We prove that the power spectrum of the tail of the CMB anisotropies on small angular scales directly gives the power spectrum of the deflection angle. We show that the generated power on small scales is correlated with the large scale gradient. The cross correlation between large scale gradient and small scale power can be used to test the hypothesis that the extra power is indeed generated by lensing. We compute the three and four point function of the temperature in the small angle limit. We relate the non-Gaussian aspects presented in this paper as well as those in our previous studies of the lensing effects on large scales to the three and four point functions. We interpret the statistics proposed in terms of different configurations of the four point function and show how they relate to the statistic that maximizes the S/N.Comment: Changes to match accepted version in PRD, 20 pages 10 figures. Better resolution images of the figures can be found at http://www.sns.ias.edu/~matiasz/RESEARCH/cmblensing.htm

Lensing Induced Cluster Signatures in Cosmic Microwave Background

We show that clusters of galaxies induce step-like wiggles on top of the cosmic microwave background (CMB). The direction of the wiggle is parallel to the large scale gradient of CMB allowing one to isolate the effect from other small scale fluctuations. The effect is sensitive to the deflection angle rather than its derivative (shear or magnification) and is thus tracing outer parts of the cluster with higher sensitivity than some other methods. A typical amplitude of the effect is $10\mu K (\sigma_v/1400 kms^{-1})^2$ where $\sigma_v$ is the velocity dispersion of the cluster and several $\mu K$ signals extend out to a fraction of a degree. We derive the expressions for the temperature profile for several simple parameterized cluster models and identify some degeneracies between parameters. Finally, we discuss how to separate this signal from other imprints on CMB using custom designed filters. Detection of this effect is within reach of the next generation of small scale CMB telescopes and could provide information about the cluster density profile beyond the virial radius.Comment: 10 pages, 3 figures, submitted to Ap

Direct Signature of Evolving Gravitational Potential from Cosmic Microwave Background

We show that time dependent gravitational potential can be directly detected from the cosmic microwave background (CMB) anisotropies. The signature can be measured by cross-correlating the CMB with the projected density field reconstructed from the weak lensing distortions of the CMB itself. The cross-correlation gives a signal whenever there is a time dependent gravitational potential. This method traces dark matter directly and has a well defined redshift distribution of the window projecting over the density perturbations, thereby avoiding the problems plaguing other proposed cross-correlations. We show that both MAP and Planck will be able to probe this effect for observationally relevant curvature and cosmological constant models, which will provide additional constraints on the cosmological parameters.Comment: 4 pages, 2 figures. Submitted to PR

Signature of Gravity Waves in Polarization of the Microwave Background

Using spin-weighted decomposition of polarization in the Cosmic Microwave Background (CMB) we show that a particular combination of Stokes $Q$ and $U$ parameters vanishes for primordial fluctuations generated by scalar modes, but does not for those generated by primordial gravity waves. Because of this gravity wave detection is not limited by cosmic variance as in the case of temperature fluctuations. We present the exact expressions for various polarization power spectra, which are valid on any scale. Numerical evaluation in inflation-based models shows that the expected signal is of the order of 0.5 $\mu K$, which could be directly tested in future CMB experiments.Comment: 4 pages, 1 figure, RevTeX, matches the accepted version (to appear in Phys. Rev. Lett.); code available at http://arcturus.mit.edu:80/~matiasz/CMBFAST/cmbfast.htm

Probing the Statistics of the Temperature-Density Relation of the IGM

Gravitational instability induces a simple correlation between the large and small scale fluctuations of the Ly-alpha flux spectrum. However, non-gravitational processes involved in structure formation and evolution will alter such a correlation. In this paper we explore how scatter in the temperature-density relation of the IGM reduces the gravitationally induced scale-scale correlation. By examining whether or not observations of the correlation are close to that predicted by pure gravity, this puts constraints on the scatter in the temperature-density relation and in turn on any physical process which would lead to scatter, e.g. strong fluctuations in the UV background or radiative transfer effects. By applying this method to high resolution Keck spectra of Q 1422+231 and HS 1946+7658, we find the predicted correlation signal induced by gravity, and the diminishing of this correlation signal at small scales. This suggests extra physics affects the small-scale structure of the forest, and we can constrain the scatter in the temperature-density relation to a conservative 20% upper limit. A crude model suggests, if there is any spatial correlation of temperature, the coherence length scale must be smaller than ~ 0.3/h Mpc to be consistent with the Keck data.Comment: 4 pages, 2 figures. Minor revisions, accepted by ApJ Letter

A Polarization Pursuers' Guide

We calculate the detectability of the polarization of the cosmic microwave background (CMB) as a function of the sky coverage, angular resolution, and instrumental sensitivity for a hypothetical experiment. We consider the gradient component of the polarization from density perturbations (scalar modes) and the curl component from gravitational waves (tensor modes). We show that the amplitude (and thus the detectability) of the polarization from density perturbations is roughly the same in any model as long as the model fits the big-bang-nucleosynthesis (BBN) baryon density and degree-scale anisotropy measurements. The degree-scale polarization is smaller (and accordingly more difficult to detect) if the baryon density is higher. In some cases, the signal-to-noise for polarization (both from scalar and tensor modes) may be improved in a fixed-time experiment with a smaller survey area.Comment: 18 pages, 6 figure