Measuring the Baryon Acoustic Oscillation scale using the SDSS and 2dFGRS

TL;DR

This work presents a general, robust framework to constrain the cosmic distance–redshift relation using Baryon Acoustic Oscillations measured from galaxy surveys spanning different redshifts. By modeling the galaxy power spectrum as a cubic spline for the smooth shape multiplied by a damped BAO component and convolving with survey windows, the authors extract r_s/D_V(z) and track D_V(z) across z without relying on a single cosmological model. Applying the method to SDSS DR5 and 2dFGRS data yields strong BAO detections at z ≈ 0.2 and z ≈ 0.35, and a joint constraint D_V(0.35)/D_V(0.2) = 1.812 ± 0.060, with r_s/D_V values of 0.1980 ± 0.0058 and 0.1094 ± 0.0033, respectively. When combined with SNLS and CMB data, the results favor a flat ΛCDM-like evolution with Ω_m ≈ 0.25–0.27 and w ≈ -1, while also offering a cross-check on the sound horizon scale and highlighting subtle tensions that warrant further investigation with future data.

Abstract

We introduce a method to constrain general cosmological models using Baryon Acoustic Oscillation (BAO) distance measurements from galaxy samples covering different redshift ranges, and apply this method to analyse samples drawn from the SDSS and 2dFGRS. BAO are detected in the clustering of the combined 2dFGRS and SDSS main galaxy samples, and measure the distance--redshift relation at z=0.2. BAO in the clustering of the SDSS luminous red galaxies measure the distance--redshift relation at z=0.35. The observed scale of the BAO calculated from these samples and from the combined sample are jointly analysed using estimates of the correlated errors, to constrain the form of the distance measure D_V(z)=[(1+z)^2D_A^2cz/H(z)]^(1/3). Here D_A is the angular diameter distance, and H(z) is the Hubble parameter. This gives r_s/D_V(0.2)=0.1980+/-0.0058 and r_s/D_V(0.35)=0.1094+/-0.0033 (1sigma errors), with correlation coefficient of 0.39, where r_s is the comoving sound horizon scale at recombination. Matching the BAO to have the same measured scale at all redshifts then gives D_V(0.35)/D_V(0.2)=1.812+/-0.060. The recovered ratio is roughly consistent with that predicted by the higher redshift SNLS supernovae data for Lambda cosmologies, but does require slightly stronger cosmological acceleration at low redshift. If we force the cosmological model to be flat with constant w, then we find Om_m=0.249+/-0.018 and w=-1.004+/-0.089 after combining with the SNLS data, and including the WMAP measurement of the apparent acoustic horizon angle in the CMB.

Figures (13)

• Figure 1: The result of fitting to $D_V(z)$ using a cubic spline fit with three nodes at $z=0.0,0.2,0.35$ for $0<z<0.5$. We plot results for three cosmological models : $\Lambda$CDM ($\hbox{$\Omega_{\rm m}$}=0.25$, $\hbox{$\Omega_\Lambda$}=0.75$, solid lines), SCDM ($\hbox{$\Omega_{\rm m}$}=1$, $\hbox{$\Omega_\Lambda$}=0$, dotted lines), and OCDM ($\hbox{$\Omega_{\rm m}$}=0.3$, $\hbox{$\Omega_\Lambda$}=0$, dashed lines). The upper panel shows the true values of $D_V(z)$ (black lines) compared with the spline fits (grey lines) with nodes (solid circles). The lower panel shows the resulting errors on $S_k$ as given by Equation (\ref{['eq:Sk']}). For the redshift range $z>0.15$, the error is $<1\%$.
• Figure 2: BAO in power spectra calculated from (a) the combined SDSS and 2dFGRS main galaxies, (b) the SDSS DR5 LRG sample, and (c) the combination of these two samples (solid symbols with $1\sigma$ errors). The data are correlated and the errors are calculated from the diagonal terms in the covariance matrix. A Standard $\Lambda$CDM distance--redshift relation was assumed to calculate the power spectra with $\hbox{$\Omega_{\rm m}$}=0.25$, $\hbox{$\Omega_\Lambda$}=0.75$. The power spectra were then fitted with a cubic spline $\times$ BAO model, assuming our fiducial BAO model calculated using CAMB, as described in Section (\ref{['sec:bao_model']}). The BAO component of the fit is shown by the solid line in each panel.
• Figure 3: As Fig. \ref{['fig:bao_lrg_main']}, but for power spectra calculated from (a) the combined SDSS DR5 LRG and main galaxy sample, (b) the SDSS main galaxy sample.
• Figure 4: Two possible ways of changing the distance--redshift model tested against the data. Dilating the scale can be achieved by simply scaling the measured power spectra and windows, while changing the form of the distance--redshift relation requires recalculation of the windows.
• Figure 5: The window function linking the input power spectrum with an observed band-power at $k=0.08\,h\,{\rm Mpc}^{-1}$ (calculated assuming a $\Lambda$CDM model), for the SDSS LRG and 2dFGRS + SDSS main galaxy catalogues. Window functions are plotted for 9 distance--redshift models with $D_V(0.2)=550\,h^{-1}\,{\rm Mpc}$ and $800<D_V(0.35)<1200\,h^{-1}\,{\rm Mpc}$. For the LRGs, the peak $k$-value of the power that contributes to this measured band--power decreases with increasing $D_V(0.35)$.