Evolution mapping: a new approach to describe matter clustering in the non-linear regime

TL;DR

This paper introduces a novel method called evolution mapping that simplifies the description of matter clustering in the non-linear regime by leveraging degeneracies in cosmological parameters, enabling faster parameter inference.

Contribution

The paper proposes a new evolution mapping approach that relates models with identical shape parameters but different evolution parameters, reducing complexity in modeling non-linear matter clustering.

Findings

Evolution mapping accurately describes non-linear power spectrum and halo mass function.

Deviations from degeneracy are explained by differences in structure formation history.

The method enables a new emulator design adaptable to various cosmological parameters.

Abstract

We present a new approach to describe statistics of the non-linear matter density field that exploits a degeneracy in the impact of different cosmological parameters on the linear dimensionless matter power spectrum, $\Delta^2_{\rm L}(k)$. We classify all cosmological parameters into two groups, shape parameters, which determine the shape of $\Delta^2_{\rm L}(k)$, and evolution parameters, which only affect its amplitude at any given redshift. With this definition, the time evolution of $\Delta^2_{\rm L}(k)$ in models with identical shape parameters but different evolution parameters can be mapped from one to the other by relabelling the redshifts that correspond to the same clustering amplitude, which we characterize by the linear mass fluctuation in spheres of radius $12\,{\rm Mpc}$, $\sigma_{12}(z)$. We use N-body simulations to show that the same evolution mapping relation gives a good description of the non-linear power spectrum, the halo mass function, or the full density field. The deviations from the exact degeneracy are the result of the different structure formation histories experienced by each model to reach the same clustering amplitude and can be accurately described in terms of differences in the suppression factor $g(a) = D(a)/a$. These relations can be used to drastically reduce the number of parameters required to describe the cosmology dependence of the power spectrum. We show how this can help to speed up the inference of parameter constraints from cosmological observations. We also present a new design of an emulator of the non-linear power spectrum whose predictions can be adapted to an arbitrary choice of evolution parameters and redshift.