Non-linear evolution of the BAO 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 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.
