The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: RSD measurement from the power spectrum and bispectrum of the DR12 BOSS galaxies (1606.00439v2)

Abstract: We measure and analyse the bispectrum of the final, Data Release 12, galaxy sample provided by the Baryon Oscillation Spectroscopic Survey, splitting by selection algorithm into LOWZ and CMASS galaxies. The LOWZ sample contains 361\,762 galaxies with an effective redshift of $z_{\rm LOWZ}=0.32$, and the CMASS sample 777\,202 galaxies with an effective redshift of $z_{\rm CMASS}=0.57$. Combining the power spectrum, measured relative to the line-of-sight, with the spherically averaged bispectrum, we are able to constrain the product of the growth of structure parameter, $f$, and the amplitude of dark matter density fluctuations, $\sigma_8$, along with the geometric Alcock-Paczynski parameters, the product of the Hubble constant and the comoving sound horizon at the baryon drag epoch, $H(z)r_s(z_d)$, and the angular distance parameter divided by the sound horizon, $D_A(z)/r_s(z_d)$. After combining pre-reconstruction RSD analyses of the power spectrum monopole, quadrupole and bispectrum monopole; with post-reconstruction analysis of the BAO power spectrum monopole and quadrupole, we find $f(z_{\rm LOWZ})\sigma_8(z_{\rm LOWZ})=0.427\pm 0.056$, $D_A(z_{\rm LOWZ})/r_s(z_d)=6.60 \pm 0.13$, $H(z_{\rm LOWZ})r_s(z_d)=(11.55\pm 0.38)10^3\,{\rm kms}^{-1}$ for the LOWZ sample, and $f(z_{\rm CMASS})\sigma_8(z_{\rm CMASS})=0.426\pm 0.029$, $D_A(z_{\rm CMASS})/r_s(z_d)=9.39 \pm 0.10$, $H(z_{\rm CMASS})r_s(z_d)=(14.02\pm 0.22)10^3\,{\rm kms}^{-1}$ for the CMASS sample. We find general agreement with previous BOSS DR11 and DR12 measurements. Combining our dataset with {\it Planck15} we perform a null test of General Relativity (GR) through the $\gamma$-parametrisation finding $\gamma=0.733^{+0.068}_{-0.069}$, which is $\sim2.7\sigma$ away from the GR predictions.

• The paper demonstrates that combining bispectrum with power spectrum analyses significantly enhances the precision of key cosmological parameters like fσ8.
• It employs a rigorous Bayesian framework with 2048 mock realizations to accurately account for survey geometry and systematic effects.
• The findings reveal a mild tension with General Relativity, underscoring the need for future surveys and refined non-linear models.

Analyzing the Bispectrum of SDSS-III BOSS DR12 Galaxies

The research paper focuses on examining the clustering of galaxies within the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) by analyzing data from the Data Release 12 (DR12). The paper measures the bispectrum, in combination with the power spectrum, from two main galaxy samples: LOWZ and CMASS. The research aims to provide constraints on several cosmological parameters, such as the product of the growth of structure parameter and the amplitude of dark matter density fluctuations ($f\sigma_8$), as well as the Alcock-Paczynski parameters; the Hubble constant multiplied by the comoving sound horizon, $H(z)r_s(z_d)$, and the angular distance parameter divided by the sound horizon, $D_A(z)/r_s(z_d)$.

The data set comprises 361,762 LOWZ galaxies and 777,202 CMASS galaxies with effective redshifts $z_{\rm LOWZ}=0.32$ and $z_{\rm CMASS}=0.57$, respectively. An entire Bayesian framework is applied to rigorously evaluate the cosmological parameters by incorporating both power spectrum and bispectrum statistics while accounting for observational effects, such as survey geometry and systematic weights.

Key Findings:

1. Cosmological Parameter Estimations:
   • For the LOWZ sample, $$f(z_{\rm LOWZ})\sigma_8(z_{\rm LOWZ})=0.460 \pm 0.071$$, $D_A(z_{\rm LOWZ})/r_s(z_d)=6.74 \pm 0.22$, and $$H(z_{\rm LOWZ})r_s(z_d)=(11.75 \pm 0.55)\cdot10^3\,{\rm km s^{-1}}$$.
   • For the CMASS sample, $$f(z_{\rm CMASS})\sigma_8(z_{\rm CMASS})=0.417 \pm 0.036$$, $D_A(z_{\rm CMASS})/r_s(z_d)=9.33 \pm 0.15$, and $$H(z_{\rm CMASS})r_s(z_d)=(13.78 \pm 0.28)\cdot10^3\,{\rm km s^{-1}}$$.
2. Inclusion of Bispectrum:
   • Integrating the bispectrum with the power spectrum multipoles enhances the constraints on $f\sigma_8$ due to the additional non-linear information provided by the bispectrum. This integration allowed researchers to break the degeneracy between $f$ and $\sigma_8$ in comparing galaxy clustering statistics.
3. Systematic Analysis:
   • Extensive tests using 2048 mock realizations revealed that the bispectrum model could accurately replicate the statistical properties observed in the data, considering both cosmic variance and systematic corrections.
4. Cosmological Implications:
   • Combining BOSS data with Planck results suggests a mild tension between the observed data and the predictions of General Relativity (GR). Specifically, the growth index parameter $\gamma$, derived using the $\gamma$-parametrization, was found to be around $2.7\sigma$ away from GR predictions.
5. Future Prospects:
   • The research highlights the necessity of further investigations using upcoming surveys with improved statistical power and the importance of refining the theoretical models to account for non-linearities more effectively.

Conclusions:

The paper presents a comprehensive analysis focusing on how the bispectrum contributes to our understanding of cosmic structure formation. By combining the power spectrum and the bispectrum, researchers can derive constraints on key cosmological parameters with higher precision, likely leading to a better understanding of the Universe's underlying physics. The findings illustrate the complementarity between different statistical measures of cosmic structure and underscore the importance of applying sophisticated modeling techniques to maximize the scientific return of large-scale galaxy surveys. Future surveys and continued advancements in non-linear modeling will be vital for addressing current tensions in cosmological parameter estimates.