Baryon Acoustic Oscillations

TL;DR

This paper surveys Baryon Acoustic Oscillations (BAO) as standard rulers for cosmology, emphasizing their linear-physics origin and robustness for mapping the expansion history via distance measures such as the angular diameter distance $d_A(z)$ and the Hubble parameter $H(z)$. It integrates theory, statistics, and observational strategies, detailing Fisher-matrix forecasting, the roles of shot noise, cosmic variance, and redshift errors, and addressing nonlinearities with bias, peak movement, and reconstruction methods that sharpen the BAO signal. The review highlights a diverse suite of tracers (LRGs, blue galaxies, Ly$\alpha$ forests, 21 cm surveys) and current/future spectroscopic and photometric surveys (e.g., SDSS, WiggleZ, BOSS, HETDEX, LSST, EUCLID, SKA), projecting percent-level distance measurements across redshifts and outlining the transformational potential for dark energy and curvature constraints. Overall, BAO are presented as a reliable, largely linear standard ruler with mature calibration paths and a broad, forward-looking survey landscape that will sharpen cosmological inferences in the coming decade.

Abstract

Baryon Acoustic Oscillations (BAO) are frozen relics left over from the pre-decoupling universe. They are the standard rulers of choice for 21st century cosmology, providing distance estimates that are, for the first time, firmly rooted in well-understood, linear physics. This review synthesises current understanding regarding all aspects of BAO cosmology, from the theoretical and statistical to the observational, and includes a map of the future landscape of BAO surveys, both spectroscopic and photometric.

Figures (21)

• Figure 1.1: The Baryon Acoustic Peak (BAP) in the correlation function -- the BAP is visible in the clustering of the SDSS LRG galaxy sample, and is sensitive to the matter density (shown are models with $\Omega_mh^2=0.12$(top), 0.13 (second) and 0.14 (third), all with $\Omega_bh^2=0.024$). The bottom line without a BAP is the correlation function in the pure CDM model, with $\Omega_b=0$. From Eisenstein et al., 2005 eisenstein_05.
• Figure 1.2: Baryon Acoustic Oscillations (BAO) in the SDSS power spectra -- the BAP of the previous figure now becomes a series of oscillations in the matter power spectrum of the SDSS sample. The power spectrum is computed for both the main SDSS sample (bottom curve) and the LRG sample (top curve), illustrating how LRGs are significantly more biased than average galaxies. The solid lines show the $\Lambda$CDM fits to the WMAP3 data wmap3, while the dashed lines include nonlinear corrections. Figure from Tegmark et al., 2006 tegmark_lrg.
• Figure 1.3: Curvature and $\chi(z)$ define cosmological distances -- In a flat Universe, the cosmological distances are determined by $\chi(z) \propto \int_0^z dz'/E(z').$ In a general FLRW model, however, spatial curvature bends the light rays away from straight lines and hence alters distances, meaning that one needs to know both $\Omega_k$ and $\chi(z)$. As a result distance measurements always show a degeneracy between curvature ($\Omega_k$) and dynamics ($H(z)$).
• Figure 1.4: Breaking the curvature-dark energy degeneracy -- Error ellipses for the CPL parameters $w_0, w_a$, in two survey scenarios after marginalising over curvature: one consisting of two measurements at $z = 1$ and $z=3$ of the angular diameter distance, with $1\%$ errors on $d_A(z)$ (blue dashed curve), and another of measurements of $H(z)$ and $d_A(z)$ (solid orange curve) where the errors have been doubled for both observables. In both surveys we assume a prior on curvature of 30, and $\mathrm{Prior}(\Omega_m) = \mathrm{Prior}(H_0) = 1000.$ Even given a weak prior on curvature, combining measurements from multiple probes helps break the curvature-dark energy degeneracy. Figure produced using Fisher4Cast.
• Figure 1.5: Rings of power superposed. Schematic galaxy distribution formed by placing the galaxies on rings of the same characteristic radius $L.$ The preferred radial scale is clearly visible in the left hand panel with many galaxies per ring. The right hand panel shows a more realistic scenario - with many rings and relatively few galaxies per ring, implying that the preferred scale can only be recovered statistically.