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Marked correlation functions, which are sensitive to the clustering ofgalaxies in different environments, have been proposed as constraints onmodified gravity models. We present measurements of the marked correlationfunctions of galaxies in redshift space using 361,761 LOWZ ($z_{\rm eff} =0.32$) galaxies from the Sloan Digital Sky Survey III (SDSS III) BaryonOscillation Spectroscopic Survey (BOSS) Data Release 12 (DR12) and compare themto $\Lambda$CDM+General Relativity simulations. We apply mass cuts to find thebest match between the redshift space autocorrelation function of subhaloes inthe simulation and in the observations. We then compare the marked correlationfunctions, finding no significant evidence for deviations of the markedcorrelation functions of LOWZ galaxies from $\Lambda$CDM on scales $6 \h^{-1}$Mpc $ \leq s \leq$ $69 \ h^{-1}$Mpc. The constraining power of markedcorrelation functions in our analysis is limited by our ability to model theautocorrelation function of galaxies on small scales including the effect ofredshift distortions. The statistical errors are well below the differencesseen between marked correlation functions of $f$(R) gravity models and$\Lambda$CDM in recent publications (Armijo et al., Hern\'{a}ndez-Aguayo etal.) indicating that improved future theoretical analyses should be able torule out some models definitively.

Measurement of marked correlation functions in SDSS-III Baryon Oscillation Spectroscopic Survey using LOWZ galaxies in Data Release 12