Redshift-space equal-time angular-averaged consistency relations of the gravitational dynamics

We present the redshift-space generalization of the equal-time angular-averaged consistency relations between $(\ell+n)$- and $n$-point polyspectra of the cosmological matter density field. Focusing on the case of $\ell=1$ large-scale mode and $n$ small-scale modes, we use an approximate symmetry of the gravitational dynamics to derive explicit expressions that hold beyond the perturbative regime, including both the large-scale Kaiser effect and the small-scale fingers-of-god effects. We explicitly check these relations, both perturbatively, for the lowest-order version that applies to the bispectrum, and nonperturbatively, for all orders but for the one-dimensional dynamics. Using a large ensemble of $N$-body simulations, we find that our squeezed bispectrum relation is valid to better than $20\%$ up to $1h$Mpc$^{-1}$, for both the monopole and quadrupole at $z=0.35$, in a $\Lambda$CDM cosmology. Additional simulations done for the Einstein-de Sitter background suggest that these discrepancies mainly come from the breakdown of the approximate symmetry of the gravitational dynamics. For practical applications, we introduce a simple ansatz to estimate the new derivative terms in the relation using only observables. Although the relation holds worse after using this ansatz, we can still recover it within $20\%$ up to $1h$Mpc$^{-1}$, at $z=0.35$ for the monopole. On larger scales, $k = 0.2 h\mathrm{Mpc}^{-1}$, it still holds within the statistical accuracy of idealized simulations of volume $\sim8h^{-3}\mathrm{Gpc}^3$ without shot-noise error.Comment: 19 pages, 4 figures. arXiv admin note: text overlap with arXiv:1311.428

RegPT: Direct and fast calculation of regularized cosmological power spectrum at two-loop order

We present a specific prescription for the calculation of cosmological power spectra, exploited here at two-loop order in perturbation theory (PT), based on the multi-point propagator expansion. In this approach power spectra are constructed from the regularized expressions of the propagators that reproduce both the resummed behavior in the high-k limit and the standard PT results at low-k. With the help of N-body simulations, we show that such a construction gives robust and accurate predictions for both the density power spectrum and the correlation function at percent-level in the weakly non-linear regime. We then present an algorithm that allows accelerated evaluations of all the required diagrams by reducing the computational tasks to one-dimensional integrals. This is achieved by means of pre-computed kernel sets defined for appropriately chosen fiducial models. The computational time for two-loop results is then reduced from a few minutes, with the direct method, to a few seconds with the fast one. The robustness and applicability of this method are tested against the power spectrum cosmic emulator from which a wide variety of cosmological models can be explored. The fortran program with which direct and fast calculations of power spectra can be done, RegPT, is publicly released as part of this paper.Comment: 28 pages, 15 figure

Testing the equal-time angular-averaged consistency relation of the gravitational dynamics in N-body simulations

We explicitly test the equal-time consistency relation between the angular-averaged bispectrum and the power spectrum of the matter density field, employing a large suite of cosmological $N$-body simulations. This is the lowest-order version of the relations between $(\ell+n)$-point and $n$-point polyspectra, where one averages over the angles of $\ell$ soft modes. This relation depends on two wave numbers, $k'$ in the soft domain and $k$ in the hard domain. We show that it holds up to a good accuracy, when $k'/k\ll 1$ and $k'$ is in the linear regime, while the hard mode $k$ goes from linear ($0.1\,h\mathrm{Mpc}^{-1}$) to nonlinear ($1.0\,h\mathrm{Mpc}^{-1}$) scales. On scales $k\lesssim 0.4\,h\mathrm{Mpc}^{-1}$, we confirm the relation within the statistical error of the simulations (typically a few percent depending on the wave number), even though the bispectrum can already deviate from leading-order perturbation theory by more than $30\%$. We further examine the relation on smaller scales with higher resolution simulations. We find that the relation holds within the statistical error of the simulations at $z=1$, whereas we find deviations as large as $\sim 7\%$ at $k \sim 1.0\,h\mathrm{Mpc}^{-1}$ at $z=0.35$. We show that this can be explained partly by the breakdown of the approximation $\Omega_\mathrm{m}/f^2\simeq1$ with supplemental simulations done in the Einstein-de Sitter background cosmology. We also estimate the impact of this approximation on the power spectrum and bispectrum.Comment: 14 pages, 15 figures, added Sec. III E and Appendixes, matched to PRD published versio

Simulating the Anisotropic Clustering of Luminous Red Galaxies with Subhalos: A Direct Confrontation with Observation and Cosmological Implications

We model the apparent clustering anisotropy of Luminous Red Galaxies (LRGs) in the Sloan Digital Sky Survey using subhalos identified in cosmological $N$-body simulations. We first conduct a Markov-chain Monte Carlo analysis on the parameters characterizing subhalos hosting LRGs assuming a specific $\Lambda$CDM cosmology on which we run the simulations. We show that simple models with central and satellite subhalos can explain the observed multipole moments of the power spectrum up to hexadecapole on large scales ($k\lesssim0.3~h\mathrm{Mpc}^{-1}$). A satellite fraction of $20$ to $30$ per cent is favored weakly depending on the detail of the model. The fraction is shown to be robust when we adopt a more refined model based on the halo occupation number from the literature. We then vary cosmological parameters controlling the anisotropy in redshift-space effectively by deforming the simulation box (the Alcock-Paczynski effect) and changing the amplitude of the velocities (the redshift-space distortions). We demonstrate that we can constrain the geometry of the universe, the structure growth rate, and the parameters characterizing LRGs simultaneously. This is a step toward cosmological analysis with realistic bias description beyond empirical bias functions with nuisance parameters.Comment: 18 pages, 21 figures. HOD analysis added. Accepted for publication in MNRA

Response function of the large-scale structure of the universe to the small scale inhomogeneities

In order to infer the impact of the small-scale physics to the large-scale properties of the universe, we use a series of cosmological $N$-body simulations of self-gravitating matter inhomogeneities to measure, for the first time, the response function of such a system defined as a functional derivative of the nonlinear power spectrum with respect to its linear counterpart. Its measured shape and amplitude are found to be in good agreement with perturbation theory predictions except for the coupling from small to large-scale perturbations. The latter is found to be significantly damped, following a Lorentzian form. These results shed light on validity regime of perturbation theory calculations giving a useful guideline for regularization of small scale effects in analytical modeling. Most importantly our result indicates that the statistical properties of the large-scale structure of the universe are remarkably insensitive to the details of the small-scale physics, astrophysical or gravitational, paving the way for the derivation of robust estimates of theoretical uncertainties on the determination of cosmological parameters from large-scale survey observations.Comment: 14 pages, 5 figures; matched to the accepted version (Physics Letters B

Cosmic shear full nulling: sorting out dynamics, geometry and systematics

An explicit full nulling scheme for cosmic shear observations is presented. It makes possible the construction of shear maps from extended source distributions for which the lens distance distribution is restricted to a definite interval. Such a construction allows to build totally independent shear maps, at all scales, that can be taken advantage of to constrain background cosmological parameters and systematics using the full statistical power of cosmic shear observations. Another advantage of such construction is that, as the lens redshift distribution can be made arbitrarily narrow, scale mixing due to projection effects can be limited allowing controlled predictions on the large scale shear power spectrum from perturbation theory calculations.Comment: 13 pages, 17 figures, accepted for publication in MNRA