Growth Rate of Cosmological Perturbations at $z\sim 0.1$ from a New Observational Test

Spatial variations in the distribution of galaxy luminosities, estimated from redshifts as distance proxies, are correlated with the peculiar velocity field. Comparing these variations with the peculiar velocities inferred from galaxy redshift surveys is a powerful test of gravity and dark-energy theories on cosmological scales. Using $\sim 2\times {10}^5$ galaxies from the SDSS Data Release 7, we perform this test in the framework of gravitational instability to estimate the normalized growth rate of density perturbations $f{\sigma }_8=0.37\pm 0.13$ at $z\sim 0.1$, which is in agreement with the cold dark matter model with a cosmological constant. This unique measurement is complementary to those obtained with more traditional methods, including clustering analysis. The estimated accuracy at $z\sim 0.1$ is competitive with other methods when applied to similar data sets.

Figure 1

(Left) Histograms of $f{\sigma }_8$ estimates (and Gaussian fits) derived with the luminosity approach from 128 mock catalogs, considering only multipoles $l>1$ (solid lines) and $l>5$ (dashed lines) in the velocity reconstructions. The distributions peak near the true value, $(f{\sigma }_8{)}_{\text{true}}\approx 0.44$, and deviate from a symmetric Gaussian mainly because of the velocity field’s nonlinear $\beta$ dependence. (Right) Estimated $\mathrm{\Delta }{\chi }^2$ (and quadratic approximations) as a function of $f{\sigma }_8$ for real SDSS galaxies and velocity models with $l>1$ (filled circles) and $l>5$ (open circles). The results assume the measured power spectrum amplitude of $L^{\star }$ galaxies from Ref. [35].

Figure 2

Comparison of growth rate measurements at low redshifts. Shown are constraints on $f{\sigma }_8$ from different redshift surveys based on RSDs [11, 37, 38, 39, 40], galaxy luminosities (filled square and circle) [24], and direct estimates of peculiar velocities (dashed, empty square) [16]. All measurements assume a fixed cosmology; the error bars indicate the respective 68% confidence intervals. The shaded areas denote the 68% and 95% confidence limits inferred from the Planck data ($\mathrm{TT}+\text{lowP}+\text{lensing}$) [36]. The square data points correspond to $z=0.02$ and are offset for clarity.