Simultaneous constraints on the growth of structure and cosmic expansion from the multipole power spectra of the SDSS DR7 LRG sample

TL;DR

We address how to jointly constrain the growth rate $f$ and expansion history $D_A$ and $H$ from the anisotropic galaxy power spectra. We employ a perturbation theory–based model (TNS) with RegPT two-loop corrections, a scale-dependent bias, and the Alcock-Paczynski effect, validated against realistic mock subhalo catalogs. Using SDSS DR7 LRG multipoles up to $\ell=4$, we obtain robust measurements at $z=0.3$ that are consistent with Planck $\Lambda$CDM, and we discuss degeneracies and systematic uncertainties. Extending the analysis to higher $k_{\max}$ reveals tensions not seen in mocks, highlighting the need for improved non-linear RSD modeling for future high-precision surveys. The approach provides a useful framework for upcoming samples (e.g., CMASS/LOWZ) and strengthens tests of gravity on cosmological scales.

Abstract

The anisotropic galaxy clustering on large scales provides us with a unique opportunity to probe into the gravity theory through the redshift-space distortions (RSDs) and the Alcock-Paczynski effect. Using the multipole power spectra up to hexadecapole (ell=4), of the Luminous Red Galaxy (LRG) sample in the data release 7 (DR7) of the Sloan Digital Sky Survey II (SDSS-II), we obtain simultaneous constraints on the linear growth rate f, angular diameter distance D_A, and Hubble parameter H at redshift z = 0.3. For this purpose, we first extensively examine the validity of a theoretical model for the non-linear RSDs using mock subhalo catalogues from N-body simulations, which are constructed to match with the observed multipole power spectra. We show that the input cosmological parameters of the simulations can be recovered well within the error bars by comparing the multipole power spectra of our theoretical model and those of the mock subhalo catalogues. We also carefully examine systematic uncertainties in our analysis by testing the dependence on prior assumption of the theoretical model and the range of wavenumbers to be used in the fitting. These investigations validate that the theoretical model can be safely applied to the real data. Thus, our results from the SDSS DR7 LRG sample are robust including systematics of theoretical modeling; f(z = 0.3) sigma_8(z = 0.3) =0.49+-0.08(stat.)+-0.04(sys.), D_A (z = 0.3) =968+-42(stat.)+-17(sys.)[Mpc], H (z = 0.3) =81.7+-5.0(stat.)+-3.7(sys.)[km/s/Mpc]. We believe that our method to constrain the cosmological parameters using subhaloes catalogues will be useful for more refined samples like CMASS and LOWZ catalogues in the Baryon Oscillation Spectroscopic Survey in SDSS-III.

Figures (10)

• Figure 1: The filled circles with error bars are the observed multipole spectra, monopole (top), quadrupole (middle), and hexadecapole (bottom) power spectra of the SDSS DR7 LRG sample. We plot the best-fitting results with solid curves, whose details are described in Section \ref{['sec:5']}. The results are multiplied by $k^{1.5}$. The best-fitting curves are plotted in the range of the wavenumbers $k\leq k_{\rm max} = 0.175 [h$/Mpc] that corresponds to the valid range of our theoretical model (see Section \ref{['sec:4.3']}). We used the data in the range of the wavenumbers $k\leq k_{\rm max} = 0.175[h$/Mpc], which include 51 data points, as described in Section \ref{['sec:5']}.
• Figure 2: Variations of monopole (top), quadrupole (middle), and hexadecapole (bottom) power spectra computed with the PT model. We plot the best-fitting model of the SDSS DR7 LRG sample in solid curves (see Section \ref{['sec:5']} and Table. \ref{['tab:systematic']}), but the other curves are the models with slightly shifting (left: increasing, right: decreasing) parameters, which characterize the linear Kaiser, FoG, and AP effects: $f$ ($\pm20\%$: (green; colors are available for the online version) dashed), $D_{\rm A}$ ($\pm10$%: (blue) dotted), $H$ ($\pm10\%$: (red) short-dotted), and $\sigma_{\rm v}$ ($\pm20\%$: (orange) dot-dashed). For reference, the measured power spectra are also plotted by filled circles with error bars.
• Figure 3: Monopole (top), quadrupole (middle), and hexadecapole (bottom) power spectra measured from our best-fitting mock catalogue and those of the SDSS DR7 LRG sample. The black solid lines correspond to our mock subhalo catalogue. The filled circles with error bars correspond to the SDSS DR7 LRG sample.
• Figure 4: Performance of our fiducial model against the mock catalogues. We plot the best-fitting parameters for WMAP5-z035 as a function of $k_{\rm max}$. The horizontal dotted lines show the fiducial values of the parameters. As is clear from this figure, the best-fitting parameters are consistent with the fiducial ones within 1-$\sigma$ error up to $k_{\rm max} = 0.175 [h$/Mpc], which is marked as the large (red; colors are available for the online version) circle. For $k_{\rm max} > 0.175 [h$/Mpc], the perturbative approach breaks down because of the non-linearity. We plot $10\chi^2$/d.o.f. in the bottom panel because we adopt the error on the power spectrum estimated for the SDSS DR7 LRG sample while the analysed mock spectra are measured from the total volume 11 times larger than the observation.
• Figure 5: Test of systematics of our analysis using the mock catalogues for estimating the linear growth rate, angular diameter distance, and Hubble parameter. The star in each panel is the fiducial input parameters. We plot the best-fitting results with symbols and 68 % confidence contours for the different setup of the analysis (symbols and contours are plotted with the same color; available for the online version) , WMAP5-z035, WMAP5-P0P2, WMAP5-z03, Planck, WMAP5-noAB, WMAP5-cbias, as noted in the figure. This figure shows that our model correctly recovers the fiducial cosmological model, and the incorrect cosmological assumptions are only marginal when taking the statistical error similar to the observed power spectra of LRGs in the SDSS DR7 into account. Note that in upper three panels, the distance scales $D_{\rm A}$ and $H$ are also normalized by the sound horizon scales at baryon drag epoch, $r_s$, to highlight a difference in the measurement of distance scales themselves. Also, the linear growth rate is scaled by $\sigma_8$. In lower three panels, the ratio $r_s/r_{s, \rm fid}$ and $\sigma_8/\sigma_{8, \rm fid}$ are unity because all the theoretical template is computed with the same underlying cosmology.