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

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 $\sigma_8$. We obtain $b_1(z_{\rm eff})^{1.40}\sigma_8(z_{\rm eff})=1.672\pm 0.060$ and $b_2^{0.30}(z_{\rm eff})\sigma_8(z_{\rm eff})=0.579\pm0.082$ at the effective redshift of the survey, $z_{\rm eff}=0.57$. The main cosmological result is the constraint on the combination $f^{0.43}(z_{\rm eff})\sigma_8(z_{\rm eff})=0.582\pm0.084$, which is complementary to $f\sigma_8$ constraints obtained from 2-point redshift space distortion analyses. A less conservative analysis yields $f^{0.43}(z_{\rm eff})\sigma_8(z_{\rm eff})=0.584\pm0.051$. 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 $f^{0.43}\sigma_8$ 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).

Analysis of SDSS DR11 BOSS Galaxy Clustering: Power Spectrum and Bispectrum

This paper investigates the clustering of galaxies from the SDSS DR11 BOSS catalog using Fourier space statistics—specifically the power spectrum and bispectrum monopoles—and aims to measure key cosmological parameters related to galaxy bias and the structure growth rate. The analysis leverages a large sample of 690,827 galaxies spanning a significant redshift range and encompassing an effective volume of approximately 6 Gpc³.

Key Objectives

1. Measurement of Galaxy Bias Parameters:
   • The study utilizes a non-linear, non-local bias model with linear (b₁) and quadratic (b₂) bias terms. This model represents a departure from conventional local bias frameworks, allowing for more accurate representation of the complex relationship between the galaxy density field and dark matter.
2. Constraint on Structure Growth Rate:
   • The research measures the growth parameter (f) and the amplitude of matter density fluctuations (σ₈), yielding constraints that complement those derived from two-point redshift-space distortion analyses.

Numerical Findings

• The effective combination of bias and growth parameters gives: b₁(z_{eff})^{1.40}σ₈(z_{eff}) = 1.672 ± 0.060 and b₂^{0.30}(z_{eff})σ₈(z_{eff}) = 0.579 ± 0.082.
• The primary cosmological result is the constraint on the combination f^{0.43}(z_{eff})σ₈(z_{eff}) = 0.582 ± 0.084, a novel constraint set from joint bispectrum and power spectrum analysis.

Theoretical and Practical Implications

• Modelling of Galaxy Bias:
  • The study incorporates sophisticated bias models, moving beyond simplistic quadratic forms to better represent the large-scale structure by accounting for non-local effects. The inclusion of non-local terms is crucial, especially given the high bias of the CMASS galaxies.
• Potential for Future Studies:
  • The paper lays groundwork for combining different clustering statistics, offering a pathway to disentangle σ₈ and f individually when paired with quadrupole analyses.
• Assessment of Systematic Reliability:
  • The research provides a thorough evaluation of systematic errors via mock catalogs and N-body simulations, ensuring robustness of the presented results.

Conclusion

The research contributes valuable insights into galaxy clustering, offering precise measurements of bias parameters and shooting to furnish a stronger handle on the growth rate of cosmic structures. Although marginal systematic underestimation is recognized and corrected, these findings demonstrate the maturity and potential of combining multi-statistic approaches to measure cosmological parameters. By employing advanced modelling techniques and extensive mock validation, the study paves the way for more holistic understanding and future developments in cosmic survey data analysis.