  The baryon acoustic oscillation (BAO) feature in the distribution of galaxies
has been widely studied as an excellent standard ruler for probing cosmic
distances and expansion history, and hence dark energy. In contrast, the
amplitude of the BAO feature has received relatively little study, mainly due
to limited signal-to-noise, and complications due to galaxy biasing, effects of
non-linear clustering and dependence on several cosmological parameters. As
expected, the amplitude of the BAO feature is sensitive to the cosmic baryon
fraction: for standard radiation content, the cosmic microwave background (CMB)
acoustic peaks constrain this precisely and the BAO amplitude is largely a
redundant cross-check. However, the CMB mainly constrains the redshift of
matter-radiation equality, z_eq, and the baryon/photon ratio: if a non-standard
radiation density N_eff is allowed, increasing N_eff while matching the CMB
peaks leads to a reduced baryon fraction and a lower relative BAO amplitude. We
construct an observable for the relative area of the BAO feature from the
galaxy correlation function (Eq.~8); from linear-theory models, we find that
this is mainly sensitive to N_eff and quite insensitive to other cosmological
parameters. More detailed work from N-body simulations will be needed to
constrain the effects of non-linearity and scale-dependent galaxy bias on this
observable.
