The Clustering of Galaxies in the SDSS-III DR9 Baryon Oscillation Spectroscopic Survey: Testing Deviations from $Λ$ and General Relativity using anisotropic clustering of galaxies (1206.5309v2)

Abstract: We use the joint measurement of geometry and growth from anisotropic galaxy clustering in the Baryon Oscillation Spectroscopic Survey Data Release 9 CMASS sample reported by Reid et al. to constrain dark energy properties and possible deviations from the General Relativity. Assuming GR and taking a prior on the linear matter power spectrum at high redshift from the cosmic microwave background (CMB), anisotropic clustering of the CMASS DR9 galaxies alone constrains $\Omega_{\rm m} = 0.308 \pm 0.022$ and $100\Omega_{\rm k} = 5.9 \pm 4.8$ for $w = -1$, or $w = -0.91 \pm 0.12$ for $\Omega_k = 0$. When combined with the full CMB likelihood, the addition of the anisotropic clustering measurements to the spherically-averaged BAO location increases the constraining power on dark energy by a factor of 4 in a flat CDM cosmology with constant dark energy equation of state $w$ (giving $w = -0.87 \pm 0.05$). This impressive gain depends on our measurement of both the growth of structure and Alcock-Paczynski effect, and is not realised when marginalising over the amplitude of redshift space distortions. Combining with both the CMB and Supernovae Type Ia (SNeIa), we find $\Omega_{\rm m} = 0.281 \pm 0.014$ and $1000\Omega_{\rm k}=-9.2\pm5.0$ for $w = -1$, or $w_0 = -1.13 \pm 0.12$ and $w_{\rm a}=0.65 \pm 0.36$ assuming $\Omega_k = 0$. Finally, when a $\Lambda$CDM background expansion is assumed, the combination of our estimate of the growth rate with previous growth measurements provides tight constraints on the parameters describing possible deviations from GR giving $\gamma = 0.64 \pm 0.05$. For one parameter extensions of the flat $\Lambda$CDM model, we find a $\sim 2\sigma$ preference either for $w > -1$ or slower growth than in GR. However, the data is fully consistent with the concordance model, and the evidence for these additional parameters is weaker than $2\sigma$.

Cosmological Implications of BOSS CMASS Clustering

The research conducted by Samushia et al. provides a thorough examination of the dark energy properties and potential deviations from General Relativity (GR) by studying the anisotropic clustering of galaxies in the BOSS CMASS sample. By utilizing the joint measurement of structure growth and geometry from these galaxies, alongside data from the cosmic microwave background (CMB), the paper offers tight constraints on dark energy (DE) and possible modifications in gravitational theory.

In terms of numerical results, one notable finding is the constraint on the matter density parameter, $\Omega_{\rm m} = 0.308 \pm 0.022$, derived under the assumption of GR with a prior obtained from the CMB linear matter power spectrum. When taking into account the possibility of a non-constant DE equation of state ($w$), the paper yields constraints of $w = -0.91 \pm 0.12$. Notably, when these measurements are combined with the full CMB likelihood, the constraining power on DE properties improves fourfold, providing $w = -0.87 \pm 0.05$ for a flat $\Lambda$CDM cosmology.

Further implications arise when considering the combination of anisotropic clustering measurements with both CMB and supernovae Type Ia data. This combination yields constraints on the cosmic expansion and structure growth parameters, $\gamma = 0.64 \pm 0.05$, which potentially suggest deviations from the GR predicted value of $\gamma \sim 0.55$.

The paper also highlights the parameter degeneracies between the gravitational growth rate and geometry, demonstrating the significance of RSD and Alcock-Paczynski effects in disentangling these. Measuring $1000\Omega_{\rm k}=-9.2\pm5.0$ for $w = -1$ underscores the model's compatibility with observations, while simultaneously implying the necessity to remain open to potential deviations from a pure $\Lambda$CDM model.

From a theoretical standpoint, the paper provides insights into the role of generalized DE models, where scalar fields with diverse potentials could mimic observational signatures akin to a cosmological constant. Furthermore, the analysis of MG manifests within the framework of scale dependence and introduces parameterizations like $\gamma$ and $\mu_s$, showing a weak yet detectable departure from standard GR.

Speculating on future developments, the integration of RSD and anisotropic clustering with upcoming high-precision datasets may augment our understanding of the cosmic acceleration and gravity models. Refining forecasts for Planck and other next-generation observational missions will prove crucial for refining these constraints, potentially allowing for more conclusive distinctions between various cosmological models.

Overall, Samushia et al.'s paper advances our understanding of the dark energy and gravitational framework underpinning our Universe, illustrating the importance of combining diverse cosmological datasets to derive more powerful constraints on the fundamental cosmological parameters.