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Author(s): Slepian, Zachary | Abstract: Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher-order corrections by integration over linear statistics of the density fields weighted by kernels resulting from recursive solution of the fluid equations. These integrals quickly become high-dimensional and naively require increasing computational resources the higher the order of the corrections. Here we show how to decouple the integrands that often produce this issue, enabling PT corrections to be computed as a sum of products of independent 1-D integrals. Our approach is related to a commonly used method for calculating multi-loop Feynman integrals in Quantum Field Theory, the Gegenbauer Polynomial $x$-Space Technique (GPxT). We explicitly reduce the three terms entering the 2-loop power spectrum, formally requiring 9-D integrations, to sums over successive 1-D radial integrals. These 1-D integrals can further be performed as convolutions, rendering the scaling of this method $N_{\rm g} \log N_{\rm g}$ with $N_{\rm g}$ the number of grid points used for each Fast Fourier Transform. This method should be highly enabling for upcoming large-scale structure redshift surveys where model predictions at an enormous number of cosmological parameter combinations will be required by Monte Carlo Markov Chain searches for the best-fit values.

Recent calculations using non-linear relativistic cosmological perturbation theory show biases in the mean luminosity distance and distance modulus at low redshift. We show that these effects may be understood very simply as a non-relativistic, and purely kinematic, Malmquist-like bias, and we describe how the effect changes if one averages over sources that are limited by apparent magnitude. This effect is essentially identical to the distance bias from small-scale random velocities that has previously been considered by astronomers, though we find that the standard formula overestimates the homogeneous bias by a factor 2.

We propose a new method to linearise cosmological mass density fields using higher order Lagrangian perturbation theory (LPT). We demonstrate that a given density field can be expressed as the sum of a linear and a nonlinear component which are tightly coupled to each other by the tidal field tensor within the LPT framework. The linear component corresponds to the initial density field in Eulerian coordinates, and its mean relation with the total field can be approximated by a logarithm (giving theoretical support to recent attempts to find such component). We also propose to use a combination of the linearisation method and the continuity equation to find the mapping between Eulerian and Lagrangian coordinates. In addition, we note that this method opens the possibility of use directly higher order LPT on nonlinear fields. We test our linearization scheme by applying it to the z~0.5 density field from an N-body simulation. We find that the linearised version of the full density field can be successfully recovered on >~5 h^{-1}Mpc, reducing the skewness and kurtosis of the distribution by about one and two orders of magnitude, respectively. This component can also be successfully traced back in time, converging towards the initial unevolved density field at z~100. We anticipate a number of applications of our results, from predicting velocity fields to estimates of the initial conditions of the universe, passing by improved constraints on cosmological parameters derived from galaxy clustering via reconstruction methods.

The peculiar motion of ionized baryons is known to introduce temperature anisotropies in the CMB by means of the kinetic Sunyaev-Zel'dovich effect (kSZ). In this work, we present an all sky computation of angular power spectrum of the temperature anisotropies introduced by kSZ momentum of all baryons in the Universe during and after reionization. In an attempt to study the bulk flows of the missing baryons not yet detected, we address separately the contribution from all baryons in the IGM and those baryons located in collapsed structures like groups and clusters of galaxies. In the first case, our approach provides a complete, all sky computation of the kSZ in second order of cosmological perturbation theory (also known as the Ostriker-Vishniac effect, OV). Most of the power of OV is generated during reionization, although it has a non-negligible tail at low redshifts, when the bulk of the kSZ peculiar momentum of the halo (cluster + group) population arises. If gas outside halos is comoving with clusters as the theory predicts, then the signature of the bulk flows of the missing baryons should be recovered by a cross-correlation analysis of future CMB data sets with kSZ estimates in clusters of galaxies. For an ACT or SPT type of CMB experiment, all sky kSZ estimates of all clusters above $2\times 10^{14} h^{-1}M_{\odot}$ should provide a detection of {\it dark} flows with signal to noise ratio (S/N) of $\sim 10$, (S/N $\sim 2.5-5$ for 2,000 - 10,000 square degrees). Improving kSZ estimates with data from Large Scale Structure surveys should enable a deeper confrontation of the theoretical predictions for bulk flows with observations. The combination of future CMB and optical data should shed light on the dark flows of the nearby, so far undetected, diffuse baryons., Comment: 18 pages, 4 pages, submitted to MNRAS, incorporating referee's comments

Cosmological Perturbation Theory (PT) is a useful tool to study the cumulants of the density and velocity fields in the large scale structure of the Universe. In Papers I & II of this series we saw that the Spherical Collapse (SC) model provides with the exact solution to PT at tree-level and gives a good approximation to the loop corrections (next to leading orders), indicating negligible tidal effects. Here, we derive predictions for the (smoothed) cumulants of the velocity divergence field $\theta \equiv \nabla\cdot\vv$ for an irrotational fluid in the SC model. By comparing with the exact analytic results by Scoccimarro & Frieman (1996), it is shown that, at least for the unsmoothed case, the loop corrections to the cumulants of $\theta$ are dominated by tidal effects. However, most of the tidal contribution seems to cancel out when computing the hierarchical ratios, $T_J = { / ^{J-1}}$. We also extend the work presented in Papers I & II to give predictions for the cumulants of the density and velocity divergence fields in non-flat spaces. In particular, we show the equivalence between the spherically symmetric solution to the equations of motion in the SC model (given in terms of the density) and that of the Lagrangian PT approach (in terms of the displacement field). It is shown that the $\Omega$-dependence is very weak for both cosmic fields even at one-loop (a 10% effect at most), except for the overall factor $f(\Omega)$ that couples to the velocity divergence., Comment: 13 pages, 8 figures. Minor changes. Accepted for publication in MNRAS