The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: On the measurement of growth rate using galaxy correlation functions

TL;DR

This study uses the CLPT-GSRSD framework to extract the linear growth rate from redshift-space distortions in the SDSS-III BOSS DR12 galaxy sample, analyzing three overlapping redshift bins. By modeling the monopole and quadrupole of the two-point correlation function via Convolution Lagrangian Perturbation Theory and Gaussian Streaming, the authors infer $f\sigma_8(z)$ along with Alcock-Paczyński parameters and distance measures, validated against MD-P mocks. The results, consistent with Planck LCDM-GR, provide robust growth-rate constraints across $0.2<z<0.75$ and demonstrate the method’s viability for gravity tests, while also contributing to the final BOSS consensus cosmology released in Alam et al. 2016. The work emphasizes the balance between exploiting quasi-linear scales for precision and avoiding strongly non-linear regimes where the model is less reliable, highlighting avenues for future small-scale RSD modeling improvements.

Abstract

We present a measurement of the linear growth rate of structure, \textit{f} from the Sloan Digital Sky Survey III (SDSS III) Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 (DR12) using Convolution Lagrangian Perturbation Theory (CLPT) with Gaussian Streaming Redshift-Space Distortions (GSRSD) to model the two point statistics of BOSS galaxies in DR12. The BOSS-DR12 dataset includes 1,198,006 massive galaxies spread over the redshift range $0.2 < z < 0.75$. These galaxy samples are categorized in three redshift bins. Using CLPT-GSRSD in our analysis of the combined sample of the three redshift bins, we report measurements of $f σ_8$ for the three redshift bins. We find $f σ_8 = 0.430 \pm 0.054$ at $z_{\rm eff} = 0.38$, $f σ_8 = 0.452 \pm 0.057$ at $z_{\rm eff} = 0.51$ and $f σ_8 = 0.457 \pm 0.052$ at $z_{\rm eff} = 0.61$. Our results are consistent with the predictions of Planck $Λ$CDM-GR. Our constraints on the growth rates of structure in the Universe at different redshifts serve as a useful probe, which can help distinguish between a model of the Universe based on dark energy and models based on modified theories of gravity. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS. The measurements and likelihoods presented here are combined with others in Alam et al. 2016 to produce the final cosmological constraints from BOSS.

Figures (7)

• Figure 1: The black dots in the plots of this figure represent monopole ($_{^{_{\blacksquare}}}$) and quadrupole ($\bullet$) for BOSS DR12 galaxy sample evaluated at different values of $s$. The error bars are obtained from the diagonal elements of the covariance matrices corresponding to mocks in the three redshift bins. The red and the blue lines denote the best fit models of monopole and quadrupole of the galaxy data. The analysis assumes a fitting range $25 \ h^{-1}$Mpc$\leq s \leq 150 \ h^{-1}$Mpc with a bin size of $5 \ h^{-1}$Mpc.
• Figure 2: The plot on the top of the figure shows the correlation matrices obtained from MD-P mocks with $z_{\rm eff}=0.38$. The plot in the center denotes the correlation matrix gotten from MD-P mocks with $z_{\rm eff}=0.51$. The plot on the bottom of the figure shows the correlation matrix obtained from MD-P mocks with $z_{\rm eff}=0.61$.
• Figure 3: Histograms of the distributions of parameters obtained from the analysis of the MD-P mocks for the three bins. We independently fit the theory to the correlation function multipoles for each of the 997 mocks (in each bin) using the covariance matrices obtained from the mocks to obtain the statistics shown in these figures. The solid blue line represents the bin corresponding to $0.2<z<0.5$ whereas the solid green line depicts the bin for the redshift range $0.4<z<0.6$. The solid red line denotes the bin with the redshift range $0.5<z<0.75$. The dashed blue, green and red lines depict Gaussian functions with zero means, unit variances and heights equal to the heights of the histograms corresponding to $z_{\rm eff} = 0.35, \ 0.51$ and $0.61$ respectively. The symbols $S_{f \sigma_8}$, $S_{||}$ and $S_{\perp}$ represent the standard deviations of the parameters $f\sigma_8$, $\alpha_{||}$ and $\alpha_{\perp}$ respectively. The x-axes of the three plots denote the ratio of the differences between the obtained parameters $f \sigma_8, \ \alpha_{||}, \ \alpha_{\perp}$ and their respective theoretical values $(f \sigma_8)^{th}, \ (\alpha_{||})^{th}, \ (\alpha_{\perp})^{th}$ with their respective standard deviations $S_{f \sigma_8}$, $S_{||}$, $S_{\perp}$. For bin1, we have $(f \sigma_8)^{th}=0.484, \ (\alpha_{||})^{th}=1.0031, \ (\alpha_{\perp})^{th}=1.0008$. For bin2, we find $(f \sigma_8)^{th}=0.483, \ (\alpha_{||})^{th}=1.0040, \ (\alpha_{\perp})^{th}=1.0010$. For bin3, we have $(f \sigma_8)^{th}=0.477, \ (\alpha_{||})^{th}=1.0046, \ (\alpha_{\perp})^{th}=1.0012$.
• Figure 4: One dimensional marginalized likelihoods for the parameters $\lbrace f \sigma_8, b \sigma_8, D_{\rm A}, H \rbrace$ for the three redshift bins. The top row depicts results of one dimensional marginalized likelihoods of parameters for the redshift bin with $0.2<z<0.5$, the middle row represents results of one dimensional marginalized likelihoods of parameters for the redshift bin with $0.4<z<0.6$ while the bottom row represents results of one dimensional marginalized likelihoods of parameters for the redshift bin with $0.5<z<0.75$. The grey shaded regions represent $1 \sigma$ spreads of the Planck $\Lambda$CDM predictions of the parameters.
• Figure 5: Here we compare our results of $f\sigma_8(z), D_{\rm A}(z)$ and $H(z)$ with the predictions of Planck $\Lambda$CDM and with the results of Beutler2016a, Grieb2016 and Sanchez2016a. The dark and the light shaded regions represent the $1 \sigma$ and the $2 \sigma$ spreads of the Planck $\Lambda$CDM (TTTEEE+lowP) predictions of $f\sigma_8, D_A$ and $H$. The solid black line shows the Planck2015 predictions for the variation of $f\sigma_8$ as a function of $z$ while the solid red line shows the predictions of Planck2016 for the variation of $f\sigma_8$ with respect to $z$.