Probing Dark Energy with Baryonic Acoustic Oscillations from Future Large Galaxy Redshift Surveys

Abstract

We show that the measurement of the baryonic acoustic oscillations in large high redshift galaxy surveys offers a precision route to the measurement of dark energy. The cosmic microwave background provides the scale of the oscillations as a standard ruler that can be measured in the clustering of galaxies, thereby yielding the Hubble parameter and angular diameter distance as a function of redshift. This, in turn, enables one to probe dark energy. We use a Fisher matrix formalism to study the statistical errors for redshift surveys up to z=3 and report errors on cosmography while marginalizing over a large number of cosmological parameters including a time-dependent equation of state. With redshifts surveys combined with cosmic microwave background satellite data, we achieve errors of 0.037 on Omega_x, 0.10 on w(z=0.8), and 0.28 on dw(z)/dz for cosmological constant model. Models with less negative w(z) permit tighter constraints. We test and discuss the dependence of performance on redshift, survey conditions, and fiducial model. We find results that are competitive with the performance of future supernovae Ia surveys. We conclude that redshift surveys offer a promising independent route to the measurement of dark energy.

Figures (9)

• Figure 1: The linear power spectrum in two different cosmological models, $\Omega_m=0.35$, $h=0.70$, and $\Omega_b=0.04$ and $\Omega_m=0.25$, $h=0.65$, and $\Omega_b=0.05$. Each power spectrum has been divided by the zero-baryon power spectrum for that $\Omega_m$ and $h$. The series of acoustic oscillations is clearly seen. Lines at the bottom show the non-linear scale, shortward of which the acoustic oscillations are washed out, as a function of redshift. The scales probed by the WMAP and Planck satellite measurements of primordial anisotropy are also shown. The error bars show the spherically averaged bandpower measurements from the $z=3$ survey we will present in § \ref{['subsec:sigmap']}.
• Figure 2: A flowchart of transformations of the Fisher matrices necessary to produce forecasts for the distance and dark energy parameters.
• Figure 3: Derivatives of angular diameter distance($D_A$) and Hubble parameter($H$) with respect to $\Omega_X$, $w_0$, and $w_1$ with $\Omega_m h^2$ being held fixed. As these are partial derivatives, one should remember that two of the three parameters are held fixed as well in each case. Notably, these are not the basis that leave the CMB anisotropies unchanged. The $\Omega_X$ parameter is equivalent to $\Omega_m$. Left: $w=-1.0$ ($\rm {\Lambda CDM}$). Right: $w=-0.667$ (Model 2).
• Figure 4: Errors on $D\!_A(z)$ and $H(z)$ as a function of $k_{\rm max}$ and $n$ for $z=1$ data set. $n$ means the baseline number density in Table \ref{['tab:con']} (about $5\times10^{-4}h^3{\rm\;Mpc}^{-3}$), and $n\times100$ means 100 times the baseline number density.
• Figure 5: Elliptical error regions on $w_0$ and $w_1$ for two different fiducial models. All other parameters have been marginalized over, and the contours are for 68% likelihood. CMB and SDSS are included in all cases.