Nonlinear evolution of the baryon acoustic oscillation scale in alternative theories of gravity

The scale of baryon acoustic oscillations (BAO) imprinted in the matter power spectrum provides an almost-perfect standard ruler: it only suffers subpercent deviations from fixed comoving length due to nonlinear 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 nonlinear 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.