Zvonimir Vlah

Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter

We develop a perturbative approach to redshift space distortions (RSD) using the phase space distribution function approach and apply it to the dark matter redshift space power spectrum and its moments. RSD can be written as a sum over density weighted velocity moments correlators, with the lowest order being density, momentum density and stress energy density. We use standard and extended perturbation theory (PT) to determine their auto and cross correlators, comparing them to N-body simulations. We show which of the terms can be modeled well with the standard PT and which need additional terms that include higher order corrections which cannot be modeled in PT. Most of these additional terms are related to the small scale velocity dispersion effects, the so called finger of god (FoG) effects, which affect some, but not all, of the terms in this expansion, and which can be approximately modeled using a simple physically motivated ansatz such as the halo model. We point out that there are several velocity dispersions that enter into the detailed RSD analysis with very different amplitudes, which can be approximately predicted by the halo model. In contrast to previous models our approach systematically includes all of the terms at a given order in PT and provides a physical interpretation for the small scale dispersion values. We investigate RSD power spectrum as a function of \mu, the cosine of the angle between the Fourier mode and line of sight, focusing on the lowest order powers of \mu and multipole moments which dominate the observable RSD power spectrum. Overall we find considerable success in modeling many, but not all, of the terms in this expansion.

On the statistics of biased tracers in the Effective Field Theory of Large Scale Structures

With the completion of the Planck mission, in order to continue to gather cosmological information it has become crucial to understand the Large Scale Structures (LSS) of the universe to percent accuracy. The Effective Field Theory of LSS (EFTofLSS) is a novel theoretical framework that aims to develop an analytic understanding of LSS at long distances, where inhomogeneities are small. We further develop the description of biased tracers in the EFTofLSS to account for the effect of baryonic physics and primordial non-Gaussianities, finding that new bias coefficients are required. Then, restricting to dark matter with Gaussian initial conditions, we describe the prediction of the EFTofLSS for the one-loop halo-halo and halo-matter two-point functions, and for the tree-level halo-halo-halo, matter-halo-halo and matter-matter-halo three-point functions. Several new bias coefficients are needed in the EFTofLSS, even though their contribution at a given order can be degenerate and the same parameters contribute to multiple observables. We develop a method to reduce the number of biases to an irreducible basis, and find that, at the order at which we work, seven bias parameters are enough to describe this extremely rich set of statistics. We then compare with the output of

Halo Zel’dovich model and perturbation theory: Dark matter power spectrum and correlation function

N

Peculiar velocities in redshift space: formalism, N-body simulations and perturbation theory

-body simulations. For the lowest mass bin, we find percent level agreement up to

Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms

k\simeq 0.3\,h\,{\rm Mpc}^{-1}

Perturbation theory, effective field theory, and oscillations in the power spectrum

for the one-loop two-point functions, and up to

Geometric and dynamic distortions in anisotropic galaxy clustering

k\simeq 0.15\,h\,{\rm Mpc}^{-1}

Nonlinear fields in generalized cosmologies

for the tree-level three-point functions, with the

Extending the modeling of the anisotropic galaxy power spectrum to k = 0.4 hMpc-1

k

Reducing the two-loop large-scale structure power spectrum to low-dimensional, radial integrals

-reach decreasing with higher mass bins. This is consistent with the theoretical estimates, and suggests that the cosmological information in LSS amenable to analytical control is much more than previously believed.