Non-linear Power Spectrum Of Dark Matter Research Articles

Enabling matter power spectrum emulation in beyond-ΛCDM cosmologies with COLA

We compare and validate COLA (COmoving Lagrangian Acceleration) simulations against existing emulators in the literature, namely Bacco and Euclid Emulator 2. Our analysis focuses on the non-linear response function, i.e., the ratio between the non-linear dark matter power spectrum in a given cosmology with respect to a pre-defined reference cosmology, which is chosen to be the Euclid Emulator 2 reference cosmology in this paper. We vary three cosmological parameters, the total matter density, the amplitude of the primordial scalar perturbations and the spectral index.By comparing the COLA non-linear response function with those computed from each emulator in the redshift range 0 ≤ z ≤ 3, we find that the COLA method is in excellent agreement with the two emulators for scales up to k ∼ 1 h/Mpc as long as the deviations of the matter power spectrum from the reference cosmology are not too large.We validate the implementation of massive neutrinos in our COLA simulations by varying the sum of neutrino masses to three different values, 0.0 eV, 0.058 eV and 0.15 eV.We show that all three non-linear prescriptions used in this work agree at the 1% level at k ≤ 1 h/Mpc. We then introduce the Effective Field Theory of Dark Energy in our COLA simulations using the N-body gauge method. We consider two different modified gravity models in which the growth of structure is enhanced or suppressed at small scales, and show that the response function with respect to the change of modified gravity parameters depends weakly on cosmological parameters in these models.

Bayesian control variates for optimal covariance estimation with pairs of simulations and surrogates

ABSTRACT Predictions of the mean and covariance matrix of summary statistics are critical for confronting cosmological theories with observations, not least for likelihood approximations and parameter inference. Accurate estimates require running costly N-body and hydrodynamics simulations. Approximate solvers, or surrogates, greatly reduce the computational cost but introduce biases, especially in the non-linear regime of structure growth. We propose ‘CARPool Bayes’ to solve the inference problem for both the means and covariances using a combination of simulations and surrogates. Our approach allows incorporating prior information for the mean and covariance. We derive closed-form solutions for maximum a posteriori covariance estimates that are efficient Bayesian shrinkage estimators, guarantee positive semidefiniteness, and can optionally leverage analytical covariance approximations. We discuss choices of the prior and propose a procedure for obtaining optimal prior hyperparameter values with a small set of test simulations. We test our method by estimating the covariances of clustering statistics of gadget-iiiN-body simulations at redshift z = 0.5 using surrogates from a 100–1000× faster particle-mesh code. Taking the sample covariance from 15 000 simulations as the truth, and using an empirical Bayes prior with diagonal blocks, our estimator produces nearly identical Fisher matrix contours for ΛCDM parameters using only 15 simulations of the non-linear dark matter power spectrum. In this case, the number of simulations is so small that the sample covariance is degenerate. We show cases where even with a naïve prior our method improves the estimate. Our framework is applicable to a wide range of cosmological problems where fast surrogates are available.

Halo model description of the non-linear dark matter power spectrum at k≫ 1 Mpc−1

Accurate knowledge of the non-linear dark-matter power spectrum is important for understanding the large-scale structure of the Universe, the statistics of dark-matter haloes and their evolution, and cosmological gravitational lensing. We analytically model the dark-matter power spectrum and its cross-power spectrum with dark-matter haloes. Our model extends the halo-model formalism, including realistic substructure population within individual dark-matter haloes and the scatter of the concentration parameter at fixed halo mass. We consider three prescriptions for the mass-concentration relation and two for the substructure distribution in dark-matter haloes. We show that this extension of the halo model mainly increases the predicted power on the small scales, and is crucial for proper modeling the cosmological weak-lensing signal due to low-mass haloes. Our extended formalism shows how the halo model approach can be improved in accuracy as one increases the number of ingredients that are calibrated from n-body simulations.

Information content in the halo-model dark-matter power spectrum — II. Multiple cosmological parameters

Abstract We investigate the cosmological Fisher information in the non-linear dark matter power spectrum in the context of the halo model. We find that there is a plateau in information content on translinear scales which is generic to all cosmological parameters we tried. There is a rise in information on smaller scales, but we find that it is quite degenerate among different cosmological parameters (except, perhaps, the tilt). This suggests that it could be difficult to constrain cosmological parameters using the non-linear regime of the dark-matter power spectrum. We suggest ways to get around this problem, such as removing the largest haloes from consideration in survey analysis.

Information content in the halo-model dark-matter power spectrum

Abstract Using the halo model, we investigate the cosmological Fisher information in the non-linear dark-matter power spectrum about the initial amplitude of linear power. We find that there is little information on ‘translinear’ scales (where the one- and two-halo terms are both significant) beyond what is on linear scales, but that additional information is present on small scales, where the one-halo term dominates. This behaviour agrees with the surprising results that Rimes & Hamilton found using N-body simulations. We argue that the translinear plateau in cumulative information arises largely from fluctuations in the numbers of large haloes in a finite volume. This implies that more information could be extracted on non-linear scales if the masses of the largest haloes in a survey are known.

Halo Properties in Models with Dynamical Dark Energy

We study the properties of dark matter (DM) halos in several models in which we have included dark energy (DE). We consider both dynamical DE, due to a scalar field self-interacting through Ratra-Peebles or supergravity potentials, and DE with constant negative w = p/ρ > -1. We find that at zero redshift, both the nonlinear power spectrum of DM and the mass function of halos do not depend appreciably on the state equation of DE, which implies that both statistics are almost indistinguishable from those of Λ-dominated cold dark matter (ΛCDM). This result is consistent with the nonlinear treatment in the accompanying paper and is also a welcome feature, because ΛCDM fits a large variety of data. On the other hand, DE halos differ from ΛCDM halos in that they are denser in their central parts, because DE halos collapsed earlier. Nevertheless, such differences are not so large. For example, the density at 10 kpc of a ~1013 M☉ DE halo is only 50% denser than the ΛCDM halo. This means that DE does not ease the problem with cuspy DM profiles. Addressing another cosmological problem, the abundance of subhalos, we find that the number of satellites of halos in various DE models does not change with respect to ΛCDM when normalized to the same circular velocity as the parent halo. Most of the above similarities are related to choosing for all models the same normalization factor σ8 at z = 0. At high redshifts, different DE and ΛCDM models have different amplitudes of fluctuations, which causes substantial deviations of halo properties to occur. Therefore, the way to find which DE equation of state gives the best fit to the observed universe is to look at the evolution of halo properties. For example, the abundance of galaxy groups with mass larger than 1013 h-1 M☉ at z ≳ 2 can be used to discriminate between the models and thus to constrain the nature of DE.