Theoretical uncertainty in baryon oscillations

TL;DR

The paper analyzes how uncertainties in the early-universe radiation content affect using baryon acoustic oscillations as a standard ruler for dark energy. It shows that the BAO scale $s$ is primarily fixed by the baryon-to-photon ratio and the redshift of matter–radiation equality $z_{\rm eq}$, with low-redshift distance measurements constraining $\sqrt{\omega_m} d_A$ and $\sqrt{\omega_m} H(z)^{-1}$ while the overall scale enters as $s \propto 1/\sqrt{\omega_m}$. Consequently, dark-energy inferences from BAO are robust to undetected relativistic components as long as $z_{\rm eq}$ is accurately determined by the CMB; misestimating $\omega_m$ mainly shifts $H_0$, and potential contributions from massive neutrinos or decays would produce small, detectable corrections. The work emphasizes the synergy between CMB measurements and BAO in constraining early-universe densities and maintaining BAO's role as a precise probe of dark energy.

Abstract

We discuss the systematic uncertainties in the recovery of dark energy properties from the use of baryon acoustic oscillations as a standard ruler. We demonstrate that while unknown relativistic components in the universe prior to recombination would alter the sound speed, the inferences for dark energy from low-redshift surveys are unchanged so long as the microwave background anisotropies can measure the redshift of matter-radiation equality, which they can do to sufficient accuracy. The mismeasurement of the radiation and matter densities themselves (as opposed to their ratio) would manifest as an incorrect prediction for the Hubble constant at low redshift. In addition, these anomalies do produce subtle but detectable features in the microwave anisotropies.

Figures (1)

• Figure 1: The angular power spectra for a fiducial $\Lambda$CDM model (solid) and three variants with a lower $z_{\rm eq}$. The dotted line shows a model with $\omega_{\rm m}$ reduced by 10%, the long dashed line $N_\nu$ increased from 3.04 to 3.78 (which raises $\rho_{\rm r}$ by 10%) and the short dashed line 10% extra $\rho_{\rm r}$ in the form of a fluid. The upper panel shows the spectra while the lower panel shows the ratio to the $\Lambda$CDM curve. All spectra have been normalized (arbitrarily) at $\ell=200$.