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We explore observational constraints on possible deviations from Newtoniangravity by means of large-scale clustering of galaxies. We measure the powerspectrum and the bispectrum of Sloan Digital Sky Survey galaxies and comparethe result with predictions in an empirical model of modified gravity. Ourmodel assumes an additional Yukawa-like term with two parameters thatcharacterize the amplitude and the length scale of the modified gravity. Themodel predictions are calculated using two methods; the second-orderperturbation theory and direct N-body simulations. These methods allow us tostudy non-linear evolution of large-scale structure. Using the simulationresults, we find that perturbation theory provides reliable estimates for thepower spectrum and the bispectrum in the modified Newtonian model. We alsoconstruct mock galaxy catalogues from the simulations, and derive constraintson the amplitude and the length scale of deviations from Newtonian gravity. Theresulting constraints from power spectrum are consistent with those obtained inour earlier work, indicating the validity of the previous empirical modeling ofgravitational nonlinearity in the modified Newtonian model. If linear biasingis adopted, the bispectrum of the SDSS galaxies yields constraints very similarto those from the power spectrum. If we allow for the nonlinear biasinginstead, we find that the ratio of the quadratic to linear biasingcoefficients, b_2/b_1, should satisfy -0.4 < b_2/b_1<0.3 in the modifiedNewtonian model.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Galaxy clustering constraints on deviations from Newtonian gravity at  cosmological scales II: Perturbative and numerical analyses of power spectrum  and bispectrum