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

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 $f{\sigma }_8(0.6)=0.48\pm 0.12$ and $f\sigma_8(0.86) = 0.48 \pm 0.10$. The additional galaxy-galaxylensing constraint alleviates galaxy bias and ${\sigma }_8$ degeneracies, providing direct measurements of $[f(0.6),{\sigma }_8(0.6)]=[0.93\pm 0.22,0.52\pm 0.06]$ and $f(0.86),{\sigma }_8(0.86)]=[0.99\pm 0.19,0.48\pm 0.04]$. 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 $\smash{\overline{E}_G}(0.6) = 0.16 \pm 0.09$and$\smash{\overline{E}_G}(0.86) = 0.09 \pm 0.07$,when$E_G$isaveragedoverscalesabove$3 h^{-1} \rm{Mpc}$\mathrm{.}Wefindthatour$E_G$ measurements exhibit slightly lower values than expected for standard relativistic gravity in a {\Lambda}CDM background, although the results are consistent within $1-2\sigma$.