On the baryon acoustic oscillation amplitude as a probe of radiation   density
  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. 
Will Sutherland and Lukasz Mularczyk (QMUL)
astro-ph.CO