Characteristic Scales of Baryon Acoustic Oscillations from Perturbation Theory: Non-linearity and Redshift-Space Distortion Effects

Abstract

An acoustic oscillation of the primeval photon-baryon fluid around the decoupling time imprints a characteristic scale in the galaxy distribution today, known as the baryon acoustic oscillation (BAO) scale. Several on-going and/or future galaxy surveys aim at detecting and precisely determining the BAO scale so as to trace the expansion history of the universe. We consider nonlinear and redshift-space distortion effects on the shifts of the BAO scale in $k$-space using perturbation theory. The resulting shifts are indeed sensitive to different choices of the definition of the BAO scale, which needs to be kept in mind in the data analysis. We present a toy model to explain the physical behavior of the shifts. We find that the BAO scale defined as in Percival et al. (2007) indeed shows very small shifts ($\lesssim$ 1%) relative to the prediction in {\it linear theory} in real space. The shifts can be predicted accurately for scales where the perturbation theory is reliable.

Figures (6)

• Figure 1: The error propagation from measured scales, $d$, to the dark energy equation of state parameter, $w_{\rm DE}$, as a function of redshift. We choose $1/H(z)$ (dotted), and $D_A(z)$ (dashed) for $d$, which correspond to the separations parallel and perpendicular to the line-of-sight direction. We also plot the three dimensional average, $(D_A^2(z)/H(z))^{1/3}$ (solid) for $d$. The shaded regions indicate the targeted redshift ranges of a future galaxy survey, WFMOS.
• Figure 2: The maximum wavenumber of the validity range for the perturbation theory, $k_{\rm 1\%}$, defined by equation (\ref{['eq:knl']}). The solid line represents the result for our fiducial model. We also plot the results for the cases with a slightly larger amplitude ($\sigma_8=0.9$; dotted), and a smaller amplitude ($\sigma_8=0.7$; dashed).
• Figure 3: The power spectrum divided by no-wiggles approximation, $f_{\rm BAO}^{\rm (i)}(k)$, in real (left) and redshift (right) spaces (see Eq.[\ref{['eq:f1']}]). The solid lines represent the results for the linear power spectrum. The others indicate the results for one-loop power spectrum at redshifts shown in the panels. The results are restricted to the range, $k\le k_{1\%}$, where the perturbation theory is safely applied (Eq.[\ref{['eq:knl']}]).
• Figure 6: The fractional shifts of peaks (from P1 to P4) and troughs (from T1 to T4) of $f_{\rm BAO}^{\rm (i)}(k)$. The left (right) panel shows the results in real (redshift) space. The two shaded regions around $z\sim1$ and $z\sim3$ are the observational windows of the planned galaxy redshift survey, WFMOS.
• Figure 9: Schematic figures of the two reasons for the shifts. The upper two curves show $f_{\rm BAO}(k)$ in case of $A'(k)=\lambda=0$, while the lowers represent those for $A'(k)>0$ (left) and $\lambda>0$ (right). The vertical thin dotted lines represent the peak and the trough positions for upper curves, while the short vertical solid lines mark those for lower curves. The shifts are given approximately by equation (\ref{['eq:model_shift']}).