Abstract:
We compute the fluctuations in gravitational lens image positions and time delay caused by large scale structure correlations. We show that these fluctuations can be expressed as a simple integral over the density power spectrum. Using the {\sl COBE} normalization we find that positions of objects at cosmological distances are expected to deviate from their true positions by a few arcminutes. These deflections are not directly observable. The positions of the images relative to one another fluctuate by a few percent of the relative separation, implying that one does not expect multiple images to be produced by large scale structures. Nevertheless, the fluctuations are larger than the observational errors on the positions and affect reconstructions of the lens potential. The time delay fluctuations have a geometrical and a gravitational contribution. Both are much larger than the expected time delay from the primary lens, but partially cancel each other. We find that large scale structure weakly affects the time delay and time delay measurements can be used as a probe of the distance scale in the universe.

Abstract:
The Rees-Sciama (RS) effect produces fluctuations in the cosmic microwave background (CMB) through the time-dependent gravitational potential in the nonlinear stages of evolution. I investigate the RS effect on the CMB angular power spectrum $C_l$ for several CDM models by combining the results of N-body simulations with second order perturbation theory. The amplitude of the RS fluctuations peaks at $l \sim 100-300$, where it gives $\Delta T /T \sim 10^{-7}-10^{-6}$ for a wide range of models. This is at least an order of magnitude below the COBE normalized primary contribution. RS fluctuations could be a dominant source of anisotropies only on subarcminute scales ($l \approx 5000$) and are below the present day observational sensitivities on all angular scales.

Abstract:
Polarization induced by cosmological scalar perturbations leads to a typical anisotropy pattern, which can best be analyzed in Fourier domain. This allows one to unambiguously distinguish cosmological signal of polarization from other foregrounds and systematics, as well as from polarization induced by non-scalar perturbations. The precision with which polarization and cross-correlation power spectra can be determined is limited by cosmic variance, noise and foreground residuals. Choice of estimator can significantly improve our capability of extracting cosmological signal and in the noise dominated limit the optimal power spectrum estimator reduces the variance by a factor of two compared to the simplest estimator. If foreground residuals are important then a different estimator can be used, which eliminates systematic effects from foregrounds so that no further foreground subtraction is needed. A particular combination of Stokes $Q$ and $U$ parameters vanishes for scalar induced polarization, thereby allowing an unambiguous determination of tensor modes. Theoretical predictions of polarization in standard models show that one typically expects a signal at the level of 5-10$\mu$K on small angular scales and around 1$\mu$K on large scales ($l<200$). Satellite missions should be able to reach sensitivities needed for an unambiguous detection of polarization, which would help to break the degeneracies in the determination of some of the cosmological parameters.

Abstract:
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.

Abstract:
We present a simple, yet accurate approximation for calculating the cosmic microwave background anisotropy power spectrum in adiabatic models. It consists of solving for the evolution of a two-fluid model until the epoch of recombination and then integrating over the sources to obtain the CMB anisotropy power spectrum. The approximation is useful both for a physical understanding of CMB anisotropies, as well as for a quantitative analysis of cosmological models. Comparison with exact calculations shows that the accuracy is typically better than 20 percent over a large range of angles and cosmological models, including those with curvature and cosmological constant. Using this approximation we investigate the dependence of the CMB anisotropies on the cosmological parameters. We identify six dimensionless parameters that uniquely determine the anisotropy power spectrum within our approximation. CMB experiments on different angular scales could in principle provide information on all these parameters. In particular, mapping of the Doppler peaks would allow an independent determination of baryon mass density, matter mass density and Hubble constant.

Abstract:
We place limits on the mean density of the universe and the slope of the linear power spectrum around a megaparsec scale by comparing the universal mass function to the observed luminosity function. Numerical simulations suggest that the dark matter halo mass function at small scales depends only on Omega_m(n_eff+3) independent of the overall power spectrum normalization. Matching the halo abundance to the observed luminosity function requires knowing the relation between the virial mass and luminosity (separately for early and late type galaxies) and the fraction of galaxies that reside in larger halos such as groups and clusters, all of which can be extracted from the galaxy-galaxy lensing. We apply the recently derived values from SDSS and find Omega_m(n_eff+3)= (0.15 \pm 0.05)/(1-f_dh), where f_dh accounts for the possibility that some fraction of halos may be dark or without a bright central galaxy. A model with Omega_m=0.25 and primordial n=0.8 or with Omega_m=0.2 and n=1 agrees well with these constraints even in the absence of dark halos, although with the current data somewhat higher values for Omega_m and n are also acceptable.

Abstract:
We present a unified approach to the problems of reconstruction of large-scale structure distribution in the universe and determination of the underlying power spectrum. These have often been treated as two separate problems and different analysis techniques have been developed for both. We show that there exists a simple relation between the optimal solutions to the two problems, allowing to solve for both within the same formalism. This allows one to apply computational techniques developed for one method to the other, which often leads to a significant reduction in the computational time. It also provides a self consistent treatment of linear reconstruction by optimally computing the power spectrum from the data itself.

Abstract:
Large-scale structure distorts the images of background galaxies, which allows one to measure directly the projected distribution of dark matter in the universe and determine its power spectrum. Here we address the question of how to extract this information from the observations. We derive minimum variance estimators for projected density reconstruction and its power spectrum and apply them to simulated data sets, showing that they give a good agreement with the theoretical minimum variance expectations. The same estimator can also be applied to the cluster reconstruction, where it remains a useful reconstruction technique, although it is no longer optimal for every application. The method can be generalized to include nonlinear cluster reconstruction and photometric information on redshifts of background galaxies in the analysis. We also address the question of how to obtain directly the 3-d power spectrum from the weak lensing data. We derive a minimum variance quadratic estimator, which maximizes the likelihood function for the 3-d power spectrum and can be computed either from the measurements directly or from the 2-d power spectrum. The estimator correctly propagates the errors and provides a full correlation matrix of the estimates. It can be generalized to the case where redshift distribution depends on the galaxy photometric properties, which allows one to measure both the 3-d power spectrum and its time evolution.

Abstract:
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).

Abstract:
We analyze scale dependence of redshift space bias $b$ and $\beta \equiv \Omega_m^{0.6}/b$ in the context of the halo model. We show that linear bias is a good approximation only on large scales, for $k<0.1h$Mpc$^{-1}$. On intermediate scales the virial motions of the galaxies cause a suppression of the power spectrum relative to the linear one, which differs from the same effect in dark matter. This suppression can potentially mimic the effect of massive neutrinos and the degeneracy can only be broken if the power spectrum is measured for $k \ll 0.1h$Mpc$^{-1}$. Different methods to determine $\beta$ converge for $k<0.1h$Mpc$^{-1}$, but give drastically different results on smaller scales, which explains some of the trends observed in the real data. We also asses the level of stochasticity by calculating the cross-correlation coefficient between the reconstructed velocity field divergence and the galaxies and show that the two fields decorrelate for $k>0.1h$Mpc$^{-1}$. Most problematic are galaxies predominantly found in groups and clusters, such as bright, red or elliptical galaxies, where we find poor convergence to a constant bias or $\beta$ even on large scales.