Non-linear evolution of the BAO scale in alternative theories of gravity

TL;DR

This paper investigates how alternative gravity theories, specifically within the Horndeski class, affect the non-linear evolution of the BAO scale, confirming its robustness as a standard ruler despite potential modifications.

Contribution

It provides the first detailed computation of the BAO shift in Horndeski theories using second-order perturbation theory, highlighting the impact of modified gravity on BAO measurements.

Findings

BAO shift is enhanced by 14-45% in covariant Galileon models.

Despite enhancement, BAO shift remains below next-generation survey precision.

Models with large BAO shifts could significantly affect redshift-space distortions and bispectrum.

Abstract

The scale of Baryon Acoustic Oscillations (BAO) imprinted in the matter power spectrum provides an almost-perfect standard ruler: it only suffers sub-percent deviations from fixed comoving length due to non-linear effects. We study the BAO shift in the large Horndeski class of gravitational theories and compute its magnitude in momentum space using second-order perturbation theory and a peak-background split. The standard prediction is affected by the modified linear growth, as well as by non-linear gravitational effects that alter the mode-coupling kernel. For covariant Galileon models, we find a $14-45\%$ enhancement of the BAO shift with respect to standard gravity and a distinct time evolution depending on the parameters. Despite the larger values, the shift remains well below the forecasted precision of next-generation galaxy surveys. Models that produce significant BAO shift would cause large redshift-space distortions or affect the bispectrum considerably. Our computation therefore validates the use of the BAO scale as a comoving standard ruler for tests of general dark energy models.