Relativistic corrections to the growth of structure in modified gravity

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 Sigma m nu = 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 similar to 10(-3) Mpc(-1) at z = 0, for a scalar field with sound speed C-s(2) similar to 0.013 during matter domination epoch. Our formalism makes it possible to test beyond Lambda CDM models probed by upcoming large-scale structure surveys on very large scales.

Automated summary

This study presents a method to introduce relativistic corrections into Horndeski theory in numerical simulations, assuming gravitational coupling only between standard matter species and the scalar field. The impact of relativistic corrections on the matter power spectrum in k-essence models, including massless and massive neutrinos, is investigated, with results showing a maximum deviation of approximately 7% at k similar to 10(-3) Mpc(-1) at z = 0. The formalism developed in this study allows for testing beyond ΛCDM models using upcoming large-scale structure surveys.