The power spectrum and bispectrum of SDSS DR11 BOSS galaxies I: bias and gravity

TL;DR

This study measures the CMASS DR11 galaxy power spectrum and bispectrum monopoles to jointly constrain galaxy bias (b1,b2) and the growth of structure (f, σ8) using a non-local Eulerian bias model and mildly non-linear perturbation theory. By combining P(k) and B(k1,k2,k3) within redshift space and implementing a robust validation suite using mock catalogs and N-body simulations, the authors derive a key constraint on f^0.43 σ8 ≈ 0.58 with substantial accuracy, and provide complementary combinations b1^1.40 σ8 and b2^0.30 σ8 that inform the galaxy-matter relation. They rigorously test systematic effects from survey geometry, redshift-space distortions, and cosmology, finding overall consistency and quantifying a small but non-negligible systematic offset in f^0.43 σ8 that is corrected in their conservative results. The work demonstrates the value of joint two- and three-point statistics for gravity and neutrino/modified gravity constraints and informs future analyses with larger surveys through improved mock realism and modeling. Overall, the paper advances precision cosmology with large-scale structure by exploiting non-local bias and mildly non-linear scales to probe gravity and bias in a complementary way to traditional fσ8 analyses.

Abstract

We analyse the anisotropic clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) CMASS Data Release 11 sample, which consists of $690 827$ galaxies in the redshift range $0.43 < z < 0.70$ and has a sky coverage of $8 498$ deg$^2$ corresponding to an effective volume of $\sim6\,\rm{Gpc}^3$. We fit the Fourier space statistics, the power spectrum and bispectrum monopoles to measure the linear and quadratic bias parameters, $b_1$ and $b_2$, for a non-linear non-local bias model, the growth of structure parameter $f$ and the amplitude of dark matter density fluctuations parametrised by $σ_8$. We obtain $b_1(z_{\rm eff})^{1.40}σ_8(z_{\rm eff})=1.672\pm 0.060$ and $b_2^{0.30}(z_{\rm eff})σ_8(z_{\rm eff})=0.579\pm0.082$ at the effective redshift of the survey, $z_{\rm eff}=0.57$. The main cosmological result is the constraint on the combination $f^{0.43}(z_{\rm eff})σ_8(z_{\rm eff})=0.582\pm0.084$, which is complementary to $fσ_8$ constraints obtained from 2-point redshift space distortion analyses. A less conservative analysis yields $f^{0.43}(z_{\rm eff})σ_8(z_{\rm eff})=0.584\pm0.051$. We ensure that our result is robust by performing detailed systematic tests using a large suite of survey galaxy mock catalogs and N-body simulations. The constraints on $f^{0.43}σ_8$ are useful for setting additional constrains on neutrino mass, gravity, curvature as well as the number of neutrino species from galaxy surveys analyses (as presented in a companion paper).

Figures (22)

• Figure 1: Power spectrum data for the NGC (blue squares) and the SGC (red circles) versions and the best fit model prediction (red and blue lines) according to NGC+SGC Planck13 (Table \ref{['tab:bestfitparams']}). Blue lines take into account the NGC mask and red lines the SGC mask. The top panel shows the power spectrum, middle panel the power spectrum normalised by a non-wiggle linear power spectrum for clarity, and the bottom panel the relative deviation of the data from the model. The black dotted lines in the bottom panel mark the 3% deviation respect to the model. In the top panel the average mocks power spectrum is indicated by the black dashed line. The model and the data show an excellent agreement within $3\%$ accuracy for the entire $k$-range displayed.
• Figure 2: Bispectrum data for NGC (blue squares) and SGC (red circles) with the best fit models (red and blue lines) listed in Table \ref{['tab:bestfitparams']} as a function of $k_3$ for given $k_1$ and $k_2$. Blue lines take into account the effects of the NGC mask, and red lines for SGC mask. For reference the (mean) bispectrum of the mock galaxy catalogs are shown by the black dashed lines. Different panels show different scales and shapes. The first row corresponds to triangles with $k_1=k_2$ whereas the second row to $k_1=2k_2$. Left column plots correspond to $k_1=0.051\,h{\rm Mpc}^{-1}$, middle column to $k_1=0.0745 \,h{\rm Mpc}^{-1}$ and the right column to $k_1=0.09 \,h{\rm Mpc}^{-1}$. The model is able to describe the observed bispectrum for $k_3\lesssim0.20\,h{\rm Mpc}^{-1}$.
• Figure 3: Reduced bispectrum for DR11 CMASS data (symbols with errors) and the corresponding model (red and blue lines) for different scales and shapes. Same notation to that in Fig. \ref{['dataBS']}. The model is able to describe the characteristic "U-shape" for scales where $k_i\lesssim0.20\,h{\rm Mpc}^{-1}$.
• Figure 4: Two dimensional distributions of the parameters of (cosmological) interest. Left panels: We use $\log_{10} b_1, \log_{10} b_2, \log_{10} f, \log_{10} \sigma_8$ to obtain simpler degeneracies. The blue points represent the best fit of the 600 NGC mock catalogs and the red cross is the best fit from the data. The mocks distributions of points have been displaced in the $\log_{10}$ space to be centered on the best fit for the NGC data. If we consider the distribution of the mocks as a sample of the posterior distribution of the parameters, the orange contour lines enclose 68% of the marginalised posterior. The green dashed lines represent the linearised direction of the degeneracy in parameter space in the region around the maximum of the distribution. The dashed red lines indicate the Planck13 cosmology. Right panels: same notation as the left panels but for the best constrained combination of parameters. The distributions appear more Gaussian than in the original variables.
• Figure 5: Best fit parameters as a function of $k_{\rm max}$ for NGC data (blue symbols), SGC data (red symbols) and a combination of both (black symbols) when the Planck13 cosmology is assumed. The quantity $f^{0.43}\sigma_8$ has been corrected by the systematic error as is listed in Table \ref{['data_table']}. For the $f^{0.43}\sigma_8$ panel, the corresponding fiducial values for GR are plotted in dashed black line. In the $A_{\rm noise}$ panel, the dotted line indicates no deviations from Poisson shot noise. The units of $\sigma_{\rm FoG}$ are Mpc$h^{-1}$. There is no apparent dependence with $k_{\rm max}$ for any of the displayed parameters for $k_{\rm max}\leq0.17\,h{\rm Mpc}^{-1}$.