Relativistic corrections to the growth of structure in modified gravity

Abstract

We present a method to introduce relativistic corrections including linear dark energy perturbations in Horndeski theory into Newtonian simulations based on the N-body gauge approach. We assume that standard matter species (cold dark matter, baryons, photons and neutrinos) are only gravitationally-coupled with the scalar field and we then use the fact that one can include modified gravity effects as an effective dark energy fluid in the total energy-momentum tensor. In order to compute the scalar field perturbations, as well as the cosmological background and metric perturbations, we use the Einstein-Boltzmann code hi class. As an example, we study the impact of relativistic corrections on the matter power spectrum in k-essence, a subclass of Horndeski theory, including the effects of massless and massive neutrinos. For massive neutrinos with m ν = 0.1 eV, the corrections due to relativistic species (photons, neutrinos and dark energy) can introduce a maximum deviation of approximately 7% to the power spectrum at k ∼ 10 −3 Mpc −1 at z = 0, for a scalar field with sound speed c 2 s ∼ 0.013 during matter domination epoch. Our formalism makes it possible to test beyond ΛCDM models probed by upcoming large-scale structure surveys on very large scales.

Fully relativistic predictions in Horndeski gravity from standard Newtonian N-body simulations

“…In the present paper we will generalize previous work [30], in which we showed how modified gravity effects can be introduced in the N-body gauge, using an effective fluid description. In this work, we will demonstrate and discuss how the full space of scalar-tensor theories described by Horndeski theory [31][32][33], can be implemented in the publicly available Einstein-Boltzmann solver hi_class [34,35], the modified gravity version of the General Relativity solver class [36,37].…”

“…The first three will be parametrized as being proportional to the fractional energy density of dark energy, α i = c i Ω DE , with i =B, M and T. The kineticity function, α K , however, will be kept constant in all cases, α K = c K . Even though we will only work with the parametric form of Horndeski's gravity, e.g., the α function parametrization of Bellini and Sawicki [48], our numerical implementation is valid for general covariant theories as well, as presented previously in [30].…”

Hi-COLA: fast, approximate simulations of structure formation in Horndeski gravity

“…Any constraints placed on the general Horndeski framework can be rapidly translated into statements about individual members of the Horndeski class. As such, constraining Horndeski gravity has emerged over the past ten years as an efficient and relatively agnostic approach for performing tests of gravity with new data [44][45][46][47][48][49][50][51][52][53][54][55]. At the level of linear perturbation theory, the popular parameterisation developed by [56], sometimes known as the effective field theory of dark energy (EFTofDE), has been successfully constrained by a variety of observations, including the binary neutron star merger GW170817 [57][58][59][60][61][62].…”

“…Having solved for the background quantities in a general reduced Horndeski theory, our next step will be to study the corresponding evolution of matter density perturbations. On large cosmological scales linear perturbation theory applies, and such modifications to the growth of structure have been computed in many gravity theories [53,[89][90][91][92][93][94]. However, in this work we are interested in pushing beyond this to the (mildly) non-linear regime.…”

Snowmass2021 Theory Frontier White Paper: Data-Driven Cosmology

“…Another simulations-based approach consists in treating the neutrinos in linear theory, while coupling to the non-linear gravitational potential of the cold dark matter [276][277][278][279][280][281]. This can make simulations with massive neutrinos only as computationally expensive as in the case of cold dark matter alone, while also accounting for all relativistic correc-tions [282][283][284].…”