Cosmic Degeneracies II: Structure formation in joint simulations of Warm Dark Matter and $f(R)$ gravity

TL;DR

This study explores the combined effects of Warm Dark Matter and $f(R)$ gravity on cosmic structure formation through novel simulations, finding limited degeneracies in most observables but notable overlaps in some specific cases.

Contribution

First simulation of joint Warm Dark Matter and $f(R)$ gravity effects on cosmological structure formation, comparing their combined impact with individual models.

Findings

Most observables show no significant degeneracy between WDM and $f(R)$ gravity.

Nonlinear matter power spectrum and halo properties are distinct for each model.

Degeneracies are observed in halo bias, redshift space power spectrum, and small void properties.

Abstract

We present for the first time the outcomes of a cosmological N-body simulation that simultaneously implements a Warm Dark Matter (WDM) particle candidate and a modified gravitational interaction in the form of $f(R)$ gravity, and compare its results with the individual effects of these two independent extensions of the standard $\Lambda $CDM scenario, and with the reference cosmology itself. We consider a rather extreme value of the WDM particle mass ($m_{\rm WDM}=0.4$ keV) and a single realisation of $f(R)$ gravity with $|\bar{f}_{R0}|=10^{-5}$, and we investigate the impact of these models and of their combination on a wide range of cosmological observables with the aim to identify possible observational degeneracies. In particular, we focus on the large-scale matter distribution, as well as on the statistical and structural properties of collapsed halos and cosmic voids. Differently from the case of combining $f(R)$ gravity with massive neutrinos -- previously investigated in Baldi et al. (2014) -- we find that most of the considered observables do not show any significant degeneracy due to the fact that WDM and $f(R)$ gravity are characterised by individual observational footprints with a very different functional dependence on cosmic scales and halo masses. In particular, this is the case for the nonlinear matter power spectrum in real space, for the halo and sub-halo mass functions, for the halo density profiles and for the concentration-mass relation. However, other observables -- like e.g. the halo bias -- do show some level of degeneracy between the two models, while a very strong degeneracy is observed for the nonlinear matter power spectrum in redshift space, for the density profiles of small cosmic voids -- with radius below $\approx 5$ Mpc$/h$ -- and for the voids abundance as a function of the void core density.