Dark Energy Constraints from Baryon Acoustic Oscillations

Baryon acoustic oscillations (BAO) in the galaxy power spectrum allows us to extract the scale of the comoving sound horizon at recombination, a cosmological standard ruler accurately determined by the cosmic microwave background anisotropy data. We examine various issues important in the use of BAO to probe dark energy. We find that assuming a flat universe, and priors on $\Omega_m$, $\Omega_m h^2$, and $\Omega_b h^2$ as expected from the Planck mission, the constraints on dark energy parameters scale much less steeply with survey area than (area)$^{-1/2}$ for a given redshift range. Dark energy constraints from BAO are very sensitive to the assumed linear scale of matter clustering and the redshift accuracy of the survey. For a BAO survey with $0.5\leq z \leq 2$, $\sigma(R)=0.4$ (corresponding to $k_{max}(z=0)=0.086 h $Mpc$^{-1}$), and $\sigma_z/(1+z)=0.001$, $({\sigma}_{w_0},{\sigma}_{w'})=$(0.115, 0.183) and (0.069, 0.104) for survey areas of 1000 (deg)$^2$ and 10000 (deg)$^2$ respectively. We find that it is critical to minimize the bias in the scale estimates in order to derive reliable dark energy constraints. For a 1000 (10000) square degree BAO survey, a 1$\sigma$ bias in $\ln H(z)$ leads to a 2$\sigma$ (3$\sigma$) bias in $w'$. The bias in $w'$ due to the same scale bias from $\ln D_A(z)$ is slightly smaller and opposite in sign. The results from this paper will be useful in assessing different proposed BAO surveys and guiding the design of optimal dark energy detection strategies