GRAVITATIONAL LENSING EFFECT ON COSMIC MICROWAVE BACKGROUND ANISOTROPIES: A POWER SPECTRUM APPROACH

The effect of gravitational lensing on cosmic microwave background (CMB) anisotropies is investigated using the power spectrum approach. The lensing effect can be calculated in any cosmological model by specifying the evolution of gravitational potential. Previous work on this subject is generalized to a non-flat universe and to a nonlinear evolution regime. Gravitational lensing cannot change the gross distribution of CMB anisotropies, but it may redistribute the power and smooth the sharp features in the CMB power spectrum. The magnitude of this effect is estimated using observational constraints on the power spectrum of gravitational potential from galaxy and cluster surveys and also using the limits on correlated ellipticities in distant galaxies. For realistic CMB power spectra the effect on CMB multipole moments is less then a few percent on degree angular scales, but gradually increases towards smaller scales. On arcminute angular scales the acoustic oscillation peaks may be partially or completely smoothed out because of the gravitational lensing.Comment: extended and corrected appendix, minor revisions of main text, revised figure

Analytic model for galaxy and dark matter clustering

We investigate an analytic model to compute nonlinear power spectrum of dark matter, galaxies and their cross-correlation. The model is based on Press-Schechter halos, which cluster and have realistic dark matter profiles. The total power spectrum is a sum of two contributions, one from correlations betwen the halos and one from correlations within the same halo. We show that such a model can give dark matter power spectra which match well with the results of N-body simulations, provided that concentration parameter decreases with the halo mass. Galaxy power spectrum differs from dark matter power spectrum because pair weighted number of galaxies increases less rapidly than the halo mass, as predicted by theoretical models and observed in clusters. In this case the resulting power spectrum becomes a power law with the slope closed to the observed. Such a model also predicts a later onset of nonlinear clustering compared to the dark matter, which is needed to reconcile the CDM models with the data. Generic prediction of this model is that bias is scale dependent and nonmonotonic. For red or elliptical galaxies bias in power spectrum may be scale dependent even on very large scales. Our predictions for galaxy-dark matter correlations, which can be observed through the galaxy-galaxy lensing, show that these cannot be interpreted simply as an average halo profile of a typical galaxy, because different halo masses dominate at different scales and because larger halos host more than one galaxy. We discuss the prospects of using cross-correlations in combination with galaxy clustering to determine the dark matter power spectrum (ABRIDGED).Comment: 16 pages, 7 figures, submitted to Phys. Rev.

Wide Angle Effects in Future Galaxy Surveys

Current and future galaxy surveys cover a large fraction of the entire sky with a significant redshift range, and the recent theoretical development shows that general relativistic effects are present in galaxy clustering on very large scales. This trend has renewed interest in the wide angle effect in galaxy clustering measurements, in which the distant-observer approximation is often adopted. Using the full wide-angle formula for computing the redshift-space correlation function, we show that compared to the sample variance, the deviation in the redshift-space correlation function from the simple Kaiser formula with the distant-observer approximation is negligible in galaxy surveys such as the SDSS, Euclid and the BigBOSS, if the theoretical prediction from the Kaiser formula is properly averaged over the survey volume. We also find corrections to the wide-angle formula and clarify the confusion in literature between the wide angle effect and the velocity contribution in galaxy clustering. However, when the FKP method is applied, substantial deviations can be present in the power spectrum analysis in future surveys, due to the non-uniform distribution of galaxy pairs.Comment: 17 pages, 11 figures, accepted for publication in MNRA

The Sunyaev-Zel'dovich angular power spectrum as a probe of cosmological parameters

The angular power spectrum of the SZ effect, C_l, is a powerful probe of cosmology. It is easier to detect than individual clusters in the field, is insensitive to observational selection effects and does not require a calibration between cluster mass and flux, reducing the systematic errors which dominate the cluster-counting constraints. It receives a dominant contribution from cluster region between 20-40% of the virial radius and is thus insensitive to the poorly known gas physics in the cluster centre, such as cooling or (pre)heating. In this paper we derive a refined analytic prediction for C_l using the universal gas-density and temperature profile and the dark-matter halo mass function. The predicted C_l has no free parameters and fits all of the published hydrodynamic simulation results to better than a factor of two around l=3000. We find that C_l scales as (sigma_8)^7 times (Omega_b h)^2 and is almost independent of all of the other cosmological parameters. This differs from the local cluster abundance studies, which give a relation between sigma_8 and Omega_m. We also compute the covariance matrix of C_l using the halo model and find a good agreement relative to the simulations. We estimate how well we can determine sigma_8 with sampling-variance-limited observations and find that for a several-square-degree survey with 1-2 arcminute resolution one should be able to determine sigma_8 to within a few percent, with the remaining uncertainty dominated by theoretical modelling. If the recent excess of the CMB power on small scales reported by the CBI experiment is due to the SZ effect, then we find sigma_8(Omega_b h/0.029)^0.3 = 1.04 +- 0.12 at the 95% confidence level (statistical) and with a residual 10% systematic (theoretical) uncertainty.Comment: 17 pages, 14 figures, 1 table, sigma8 constraint including CBI and BIMA, matches the accepted version in MNRA

A Line of Sight Approach to Cosmic Microwave Background Anisotropies

We present a new method for calculating linear cosmic microwave background (CMB) anisotropy spectra based on integration over sources along the photon past light cone. In this approach the temperature anisotropy is written as a time integral over the product of a geometrical term and a source term. The geometrical term is given by radial eigenfunctions which do not depend on the particular cosmological model. The source term can be expressed in terms of photon, baryon and metric perturbations, all of which can be calculated using a small number of differential equations. This split clearly separates between the dynamical and geometrical effects on the CMB anisotropies. More importantly, it allows to significantly reduce the computational time compared to standard methods. This is achieved because the source term, which depends on the model and is generally the most time consuming part of calculation, is a slowly varying function of wavelength and needs to be evaluated only in a small number of points. The geometrical term, which oscillates much more rapidly than the source term, does not depend on the particular model and can be precomputed in advance. Standard methods that do not separate the two terms and require a much higher number of evaluations. The new method leads to about two orders of magnitude reduction in CPU time when compared to standard methods and typically requires a few minutes on a workstation for a single model. The method should be especially useful for accurate determinations of cosmological parameters from CMB anisotropy and polarization measurements that will become possible with the next generation of experiments. A programm implementing this method can be obtained from the authors.Comment: 20 pages, 5 figures. Fortran code available from the author