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The clustering ratio $\eta$, a large-scale structure observable originallydesigned to constrain the shape of the power spectrum of matter densityfluctuations, is shown to provide a sensitive probe of the nature of gravity inthe cosmological regime. We apply this analysis to $F(R)$ theories of gravityusing the luminous red galaxy (LRG) sample extracted from the spectroscopicSloan Digital Sky Survey (SDSS) data release 7 and 10 catalogues. We find thatGeneral Relativity (GR), complemented with a Friedmann-Robertson-Walker (FRW)cosmological model with parameters fixed by the Planck satellite, describesextremely well the clustering of galaxies up to $z\sim 0.6$. On large cosmicscales, the absolute amplitude of deviations from GR, $|f_{R_0 }|$, isconstrained to be smaller than $4.6 \times 10^{-5}$ at the $95\%$ confidencelevel. This bound makes cosmological probes of gravity almost competitive withthe sensitivity of Solar System tests, although still one order of magnitudeless effective than astrophysical tests. We also extrapolate our results tofuture large surveys like Euclid and show that the astrophysical bound willcertainly remain out of reach for such a class of modified-gravity models thatonly differ from $\Lambda$CDM at low redshifts.

Cosmological tests of modified gravity: constraints on $F(R)$ theories from the galaxy clustering ratio