The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: measuring structure growth using passive galaxies

TL;DR

The paper addresses how to improve measurements of the growth of cosmic structure by exploiting a passively evolving galaxy population to break degeneracies between growth rate, bias, and $\\sigma_8$. It develops a model that ties bias evolution to passive evolution (Fry96) and parameterizes $\\sigma_8(z)$ with redshift-node values, fitting the redshift-space monopole and quadrupole of the correlation function across SDSS-I/II and SDSS-III data. The passive-bias approach yields up to ~1.5x tighter constraints on $\\sigma_8(0)$ than a free-growth model, with results compatible with $\\Lambda$CDM and GR, suggesting strong potential for precision growth mapping with current and future data. The method demonstrates a practical path to high-precision growth measurements by combining careful sample matching, luminosity weighting, and bias-evolution priors, paving the way for extensions to higher redshift and larger surveys.

Abstract

We explore the benefits of using a passively evolving population of galaxies to measure the evolution of the rate of structure growth between z=0.25 and z=0.65 by combining data from the SDSS-I/II and SDSS-III surveys. The large-scale linear bias of a population of dynamically passive galaxies, which we select from both surveys, is easily modeled. Knowing the bias evolution breaks degeneracies inherent to other methodologies, and decreases the uncertainty in measurements of the rate of structure growth and the normalization of the galaxy power-spectrum by up to a factor of two. If we translate our measurements into a constraint on sigma_8(z=0) assuming a concordance cosmological model and General Relativity (GR), we find that using a bias model improves our uncertainty by a factor of nearly 1.5. Our results are consistent with a flat Lambda Cold Dark Matter model and with GR.

Figures (3)

• Figure 1: Black curves in all panels show the marginalised likelihood distributions of our fitted and derived parameters. The fitted parameters are $b_{z_0}$ (first panel) and $\sigma_8(z_{nodes})$ (second panel, with $z_{node} = 0, 0.3$ and $0.6$ from right to left). The derived parameters are $f(z)$, $f(z)\sigma_8(z)$ and $b(z)\sigma_8(z)$. Vertical solid red lines show the best-fit values, and the vertical dot-dashed red lines the $1\sigma$ confidence intervals. Top right two panels show the measured value of $A_{0,2}(z)$ (black circles) and $1\sigma$ errors - the red line shows the best fit model. Dashed blue lines throughout show predictions from ${\Lambda}$CDM and GR, using the best-fit values for the fitted parameters. GR is perfectly compatible with our measurements of the growth rate.
• Figure 2: Evolution of $f\sigma_8$ as a function of redshift for the passive model and free growth. The black data points are from: BlakeEtAl11RSD, PercivalEtAl04RSD, TegmarkEtAl06 and GuzzoEtAl08; as collected by SongEtAl09. We also show measurements from SamushiaEtAl12 and from ReidEtAl12. For completeness we also show the measurements of DavisEtAl11 and TurnbullEtAl12 from peculiar velocities at $z=0.02$, as compiled by HudsonEtAl12. The smooth solid line shows the prediction of ${\Lambda}$CDM and GR, using a WMAP7 cosmology with $\sigma_8 (z=0) = 0.81$.
• Figure 3: Constraints on $\sigma_8(z=0)$ from the data points in Fig. \ref{['fig:fs8_ev']}, assuming ${\Lambda}$CDM and GR. The vertical shaded bar shows the constraints placed by the joint data analysis in WMAP7 KomatsuEtAl11. The constraints from the passive model are approximately 1.5 times better than a free growth model, and competitive relative to ReidEtAl12 on the full CMASS sample. On the left we show the dataset used for each measurement.