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

TL;DR

This paper extends the N-body gauge framework to Horndeski gravity, enabling relativistic effects to be incorporated into Newtonian simulations, revealing gravity acoustic oscillations as a new relativistic signature in the matter power spectrum.

Contribution

It introduces a method to include relativistic effects from Horndeski gravity in Newtonian N-body simulations, highlighting the emergence of gravity acoustic oscillations as a novel relativistic phenomenon.

Findings

Relativistic effects can be incorporated as an additional linear density field in simulations.

Gravity acoustic oscillations appear at large scales due to scalar field dynamics.

GAOs could be detectable with future galaxy and intensity-mapping surveys.

Abstract

The N-body gauge allows the introduction of relativistic effects in Newtonian cosmological simulations. Here we extend this framework to general Horndeski gravity theories, and investigate the relativistic effects that the scalar field introduces in the matter power spectrum at intermediate and large scales. In particular, we show that the kineticity function at these scales enhances the amplitude of the signal of contributions coming from the extra degree of freedom. Using the Quasi-Static Approximation (QSA), we separate modified gravity effects into two parts: one that only affects small-scale physics, and one that is due to relativistic effects. This allows our formalism to be readily implemented in modified gravity N-body codes in a straightforward manner, e.g., relativistic effects can be included as an additional linear density field in simulations. We identify the emergence of gravity acoustic oscillations (GAOs) in the matter power spectrum at large scales, $k \sim 10^{-3}-10^{-2}$ Mpc$^{-1}$. GAO features have a purely relativistic origin, coming from the dynamical nature of the scalar field. GAOs may be enhanced to detectable levels by the rapid evolution of the dark energy sound horizon in certain modified gravity models and can be seen as a new test of gravity at scales probed by future galaxy and intensity-mapping surveys.