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

Polarization of the Microwave Background in Defect Models

We compute the polarization power spectra for global strings, monopoles, textures and nontopological textures, and compare them to inflationary models. We find that topological defect models predict a significant (1 microK) contribution to magnetic type polarization on degree angular scales, which is produced by the large vector component of the defect source. We also investigate the effect of decoherence on polarization. It leads to a smoothing of acoustic oscillations both in temperature and polarization power spectra and strongly suppresses the cross-correlation between temperature and polarization relative to inflationary models. Presence or absence of magnetic polarization or cross-correlation would be a strong discriminator between the two theories of structure formation and will be testable with the next generation of CMB satellites.Comment: 4 pages, 3 figures, RevTeX fil

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

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

Power Spectra in Global Defect Theories of Cosmic Structure Formation

An efficient technique for computing perturbation power spectra in field ordering theories of cosmic structure formation is introduced, enabling computations to be carried out with unprecedented precision. Large scale simulations are used to measure unequal time correlators of the source stress energy, taking advantage of scaling during matter and radiation domination, and causality, to make optimal use of the available dynamic range. The correlators are then re-expressed in terms of a sum of eigenvector products, a representation which we argue is optimal, enabling the computation of the final power spectra to be performed at high accuracy. Microwave anisotropy and matter perturbation power spectra for global strings, monopoles, textures and non-topological textures are presented and compared with recent observations.Comment: 4 pages, compressed and uuencoded RevTex file and postscript figure

Classification of singular points in polarization field of CMB and eigenvectors of Stokes matrix

Analysis of the singularities of the polarization field of CMB, where polarization is equal to zero, is presented. It is found that the classification of the singular points differs from the usual three types known in the ordinary differential equations. The new statistical properties of polarization field are discussed, and new methods to detect the presence of primordial tensor perturbations are indicated.Comment: 7 pages, 1 figure

Reconstructing Projected Matter Density from Cosmic Microwave Background

Gravitational lensing distorts the cosmic microwave background (CMB) anisotropies and imprints a characteristic pattern onto it. The distortions depend on the projected matter density between today and redshift $z \sim 1100$. In this paper we develop a method for a direct reconstruction of the projected matter density from the CMB anisotropies. This reconstruction is obtained by averaging over quadratic combinations of the derivatives of CMB field. We test the method using simulations and show that it can successfully recover projected density profile of a cluster of galaxies if there are measurable anisotropies on scales smaller than the characteristic cluster size. In the absence of sufficient small scale power the reconstructed maps have low signal to noise on individual structures, but can give a positive detection of the power spectrum or when cross correlated with other maps of large scale structure. We develop an analytic method to reconstruct the power spectrum including the effects of noise and beam smoothing. Tests with Monte Carlo simulations show that we can recover the input power spectrum both on large and small scales, provided that we use maps with sufficiently low noise and high angular resolution.Comment: 21 pages, 9 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

The Case for an Accelerating Universe from Supernovae

The unexpected faintness of high-redshift Type Ia supernovae (SNe Ia), as measured by two teams, has been interpreted as evidence that the expansion of the Universe is accelerating. We review the current challenges to this interpretation and seek to answer whether the cosmological implications are compelling. We discuss future observations of SNe Ia which could offer extraordinary evidence to test acceleration.Comment: To appear as an Invited Review for PASP 20 pages, 13 figure