Testing Gravity with the CFHTLS-Wide Cosmic Shear Survey and SDSS LRGs

TL;DR

The paper tests general relativity on cosmological scales by constraining modifications to the Poisson equation using cosmic shear from CFHTLS-Wide and galaxy clustering from SDSS LRGs. It adopts two phenomenological gravity models, Yukawa and Uzan-Bernardeau, parameterized by $(\alpha,m)$ and $(r_s)$, and infers how they alter the linear growth factor through a modified growth equation $\ddot D+2H\dot D=\frac{3}{2}\frac{H_0^2\Omega_{m0}}{a^3} f(k) D$. A joint likelihood with priors on the amplitude $A_s$ and nuisance parameters, and cross-checks with two non-linear prescriptions and two lensing statistics, yields no detectable deviation from GR on scales $0.04$–$10$ Mpc at low redshift, with SDSS providing tighter constraints due to larger sky coverage. The results translate into lower bounds on the graviton mass in the Yukawa case (e.g., $1/m \gtrsim$ a few to tens of Mpc for various $\alpha$) and on the UB scale $r_s$, and highlight the need for tomography and larger surveys to improve sensitivity.

Abstract

General relativity as one the pillar of modern cosmology has to be thoroughly tested if we want to achieve an accurate cosmology. We present the results from such a test on cosmological scales using cosmic shear and galaxy clustering measurements. We parametrize potential deviation from general relativity as a modification to the cosmological Poisson equation. We consider two models relevant either for some linearized theory of massive gravity or for the physics of extra-dimensions. We use the latest observations from the CFHTLS-Wide survey and the SDSS survey to set our constraints. We do not find any deviation from general relativity on scales between 0.04 and 10 Mpc. We derive constraints on the graviton mass in a restricted class of model.

Figures (5)

• Figure 1: Ratio of linear growth factor of modified gravity versus $\Lambda$CDM at $z=0$. From left to right, the Yukawa model and the UB model.
• Figure 2: Likelihood contours at 68% and 95% confidence levels for the $1/m$ and $\alpha$ parameters of the Yukawa type modification to gravity. The left panel corresponds to the CFHTLS-Wide constrains while the right panel corresponds to SDSS LRGs. Colored contours correspond for CFTHSL-Wide to the use of the $M_{ap}^2$ statistic with the halofit non-linear prescription. The dashed lines were obtained using the $M_{ap}^2$ statistic with the peacock96 prescription whereas the dot-dashed lines were obtained with the halofit non-linear prescription but using the $\xi_E$ statistic. The agreement between these various prescriptions and statistics is a satisfying of robustness of our measurement. As expected given the wider area covered by SDSS (42 times bigger than the current status of CFHTLS-Wide), the SDSS constraints are much narrower despite the bias uncertainty.
• Figure 3: Likelihood contours at 68% and 95% confidence levels for the normalisation parameter $A_s$ and $\alpha$ parameter of the Yukawa type modification to gravity. We consider for this plot only $1/m \le 0.1$Mpc so that we explore the lower part of the left plot in Fig. \ref{['fig:contours_wl_lrg']}. This plot illustrate the degeneracy between $\alpha$ and $A_s$ that is expected given Fig. \ref{['fig:ratio_D']} where we can see that for a given $m$ and redshift, $\alpha$ will change the amplitude of $P(k)$ above a given scale.
• Figure 4: 1D likelihood distribution for $\alpha$ when one sets $1/m=0.04$Mpc. Likelihood corresponds to either CFHTLS-Wide or SDSS. Vertical lines correspond to 68% and 95% confidence levels. We can see that for this scale, CFHTLS-Wide constraints are only $\simeq$2 times worse than SDSS ones. This can be understood from the fact that lensing is sensitive to the overall normalization of the power spectrum.
• Figure 5: $r_s$ likelihood distribution for the UB model. Vertical lines correspond to 68% and 95% confidence levels. Blue lines correspond to CFHLS-Wide constraints whereas red lines correspond to SDSS. The blue dashed line corresponds to the use of the peacock96 prescription to model non-linearities while the solid line corresponds to the smith03halofit prescription.