The VIMOS Public Extragalactic Redshift Survey (VIPERS). Gravity test from the combination of redshift-space distortions and galaxy-galaxy lensing at $0.5<z<1.2$

Abstract

We carry out a joint analysis of redshift-space distortions and galaxy-galaxy lensing, with the aim of measuring the growth rate of structure; this is a key quantity for understanding the nature of gravity on cosmological scales and late-time cosmic acceleration. We make use of the final VIPERS redshift survey dataset, which maps a portion of the Universe at a redshift of $z\simeq 0.8$, and the lensing data from the CFHTLenS survey over the same area of the sky. We build a consistent theoretical model that combines non-linear galaxy biasing and redshift-space distortion models, and confront it with observations. The two probes are combined in a Bayesian maximum likelihood analysis to determine the growth rate of structure at two redshifts $z=0.6$ and $z=0.86$. We obtain measurements of $f\ddot{I}{ƒ}_8(0.6)=0.48\pm 0.12$ and $f\ddot{I}{ƒ}_8(0.86)=0.48\pm 0.10$. The additional galaxy-galaxylensing constraint alleviates galaxy bias and $\ddot{I}{ƒ}_8$ degeneracies, providing direct measurements of $[f(0.6),\ddot{I}{ƒ}_8(0.6)]=[0.93\pm 0.22,0.52\pm 0.06]$ and $f(0.86),\ddot{I}{ƒ}_8(0.86)]=[0.99\pm 0.19,0.48\pm 0.04]$. These measurements are statistically consistent with a Universe where the gravitational interactions can be described by General Relativity, although they are not yet accurate enough to rule out some commonly considered alternatives. Finally, as a complementary test we measure the gravitational slip parameter, $E_G$ , for the first time at $z>0.6$. We find values of ${\overline{E}}_G(0.6)=0.16\pm 0.09$ and ${\overline{E}}_G(0.86)=0.09\pm 0.07$, when $E_G$ is averaged over scales above $3h^{-1}\mathrm{Mpc}$. We find that our $E_G$ measurements exhibit slightly lower values than expected for standard relativistic gravity in a ΛCDM background, although the results are consistent within $1-2\ddot{I}ƒ$.

21 pages, 19 figures, accepted for publication in A&A (referee report received seven months after submission)