Time-Delay Effect on the cOsmic Background Radiation by Static Gravitational Potential of Clusters

We present a quantitative analysis of the time-delay effect on the cosmic background radiation (CBR) by static gravitational potential of galaxy clusters. This is primarily motivated by growing observational evidence that clusters have essentially experienced no-evolution since redshift $z\approx1$, indicating that the contribution of a time-dependent potential to CBR anisotropy discussed in literature could be rather small for the dynamically-relaxed clusters. Using the softened isothermal sphere model and the universal density profile for the mass distribution of rich clusters, we calculate the CBR anisotropy by the time-delay effect and compare it with those generated by the thermal and kinematic S-Z effects as well as by the transverse motion of clusters. While it is unlikely that the time-delay effect is detectable in the current S-Z measurement because of its small amplitude of $10^{-6}$-$10^{-7}$ and its achromaticity, it nevertheless leads to an uncertainty of $\sim10$ in the measurement of the kinematic S-Z effect of clusters. Future cosmological application of the peculiar velocity of clusters to be measured through the S-Z effect should therefore take this uncertainty into account.Comment: 15pages,1figures,accepted by Astrophysical Journa

Contributions to the Power Spectrum of Cosmic Microwave Background from Fluctuations Caused by Clusters of Galaxies

We estimate the contributions to the cosmic microwave background radiation (CMBR) power spectrum from the static and kinematic Sunyaev-Zel'dovich (SZ) effects, and from the moving cluster of galaxies (MCG) effect. We conclude, in agreement with other studies, that at sufficiently small scales secondary fluctuations caused by clusters provide important contributions to the CMBR. At $\ell \gtrsim 3000$, these secondary fluctuations become important relative to lensed primordial fluctuations. Gravitational lensing at small angular scales has been proposed as a way to break the ``geometric degeneracy'' in determining fundamental cosmological parameters. We show that this method requires the separation of the static SZ effect, but the kinematic SZ effect and the MCG effect are less important. The power spectrum of secondary fluctuations caused by clusters of galaxies, if separated from the spectrum of lensed primordial fluctuations, might provide an independent constraint on several important cosmological parameters.Comment: LateX, 41 pages and 10 figures. Accepted for publication in the Astrophysical Journa

Extragalactic Foregrounds of the Cosmic Microwave Background: Prospects for the MAP Mission

(Abridged) While the major contribution to the Cosmic Microwave Background (CMB) anisotropies are the sought-after primordial fluctuations produced at the surface of last scattering, other effects produce secondary fluctuations at lower redshifts. Here, we study the extragalactic foregrounds of the CMB in the context of the upcoming MAP mission. We first survey the major extragalactic foregrounds and show that discrete sources, the Sunyaev-Zel'dovich (SZ) effect, and gravitational lensing are the most dominant ones for MAP. We then show that MAP will detect (>5 sigma) about 46 discrete sources and 10 SZ clusters directly with 94 GHz fluxes above 2 Jy. The mean SZ fluxes of fainter clusters can be probed by cross-correlating MAP with cluster positions extracted from existing catalogs. For instance, a MAP-XBACs cross-correlation will be sensitive to clusters with S(94GHz)>200mJy, and will thus provide a test of their virialization state and a measurement of their gas fraction. Finally, we consider probing the hot gas on supercluster scales by cross-correlating the CMB with galaxy catalogs. Assuming that galaxies trace the gas, we show that a cross-correlation between MAP and the APM catalog should yield a marginal detection, or at least a four-fold improvement on the COBE upper limits for the rms Compton y-parameter.Comment: 27 LaTeX pages, including 5 ps figures and 2 tables. To appear in ApJ. Minor revisions to match accepted version. Color figures and further links available at http://www.astro.princeton.edu/~refreg

Cosmic Microwave Background anisotropies from second order gravitational perturbations

This paper presents a complete analysis of the effects of second order gravitational perturbations on Cosmic Microwave Background anisotropies, taking explicitly into account scalar, vector and tensor modes. We also consider the second order perturbations of the metric itself obtaining them, for a universe dominated by a collision-less fluid, in the Poisson gauge, by transforming the known results in the synchronous gauge. We discuss the resulting second order anisotropies in the Poisson gauge, and analyse the possible relevance of the different terms. We expect that, in the simplest scenarios for structure formation, the main effect comes from the gravitational lensing by scalar perturbations, that is known to give a few percent contribution to the anisotropies at small angular scales.Comment: 15 pages, revtex, no figures. Version to be published in Phys. Rev.

The Effect of Weak Gravitational Lensing on the Cosmic Microwave Background Anisotropy: Flat versus Open Universes

We have studied the effect of gravitational lensing on the Cosmic Microwave Background (CMB) anisotropy in flat and open universes. We develop a formalism to calculate the changes on the radiation power spectrum induced by lensing in the Newtonian and synchronous-comoving gauges. The previously considered negligible contribution to the CMB radiation power spectrum of the anisotropic term of the lensing correlation is shown to be appreciable. However, considering the nonlinear evolution of the matter power spectrum produces only slight differences on the results based on linear evolution. The general conclusion for flat as well as open universes is that lensing slightly smoothes the radiation power spectrum. For a given range of multipoles the effect of lensing increases with Omega but for the same acoustic peak it decreases with $\Omega$. The maximum contribution of lensing to the radiation power spectrum for $l\leq 2000$ is $\sim$ 5% for $\Omega$ values in the range 0.1-1.Comment: latex file in ApJ style, 17 pages, 3 ps figure

Non-linear Integrated Sachs-Wolfe Effect

We discuss the non-linear extension to the integrated Sachs-Wolfe effect (ISW) resulting from the divergence of the large scale structure momentum density field. The non-linear ISW effect leads to an increase in the total ISW contribution by roughly two orders of magnitude at l ~ 1000. This increase, however, is still below the cosmic variance limit of the primary anisotropies; at further small angular scales, secondary effects such as gravitational lensing and the kinetic Sunyaev-Zel'dovich (SZ) effect dominates the non-linear ISW power spectrum. We show this second-order non-linear ISW contribution is effectively same as the contribution previously described as a lensing effect due to the transverse motion of gravitational lenses and well known as the Kaiser-Stebbins effect under the context of cosmic strings. Due to geometrical considerations, there is no significant three point correlation function, or a bispectrum, between the linear ISW effects and its non-linear extension. The non-linear ISW contribution can be potentially used as a probe of the transverse velocity of dark matter halos such as galaxy clusters. Due to the small contribution to temperature fluctuations, of order few tenths of micro Kelvin, however, extrating useful measurements on velocities will be challenging.Comment: 12 pages, 8 figures; submitted to Phys. Rev.

The integrated Sachs-Wolfe Effect -- Large Scale Structure Correlation

We discuss the correlation between late-time integrated Sachs-Wolfe (ISW) effect in the cosmic microwave background (CMB) temperature anisotropies and the large scale structure of the local universe. This correlation has been proposed and studied in the literature as a probe of the dark energy and its physical properties. We consider a variety of large scale structure tracers suitable for a detection of the ISW effect via a cross-correlation. In addition to luminous sources, we suggest the use of tracers such as dark matter halos or galaxy clusters. A suitable catalog of mass selected halos for this purpose can be constructed with upcoming wide-field lensing and Sunyaev-Zel'dovich (SZ) effect surveys. With multifrequency data, the presence of the ISW-large scale structure correlation can also be investigated through a cross-correlation of the frequency cleaned SZ and CMB maps. While convergence maps constructed from lensing surveys of the large scale structure via galaxy ellipticities are less correlated with the ISW effect, lensing potentials that deflect CMB photons are strongly correlated and allow, probably, the best mechanism to study the ISW-large scale structure correlation with CMB data alone.Comment: 10 Pages, PRD submitte

Higher-Order Gravitational Perturbations of the Cosmic Microwave Background

We study the behavior of light rays in perturbed Robertson-Walker cosmologies, calculating the redshift between an observer and the surface of last scattering to second order in the metric perturbation. At first order we recover the classic results of Sachs and Wolfe, and at second order we delineate the various new effects which appear; there is no {\it a priori} guarantee that these effects are significantly smaller than those at first order, since there are large length scales in the problem which could lead to sizable prefactors. We find that second order terms of potential observational interest may be interpreted as transverse and longitudinal lensing by foreground density perturbations, and a correction to the integrated Sachs-Wolfe effect.Comment: 21 pages, one figure; minor corrections, new reference