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

We explore observational constraints on possible deviations from Newtonian gravity by means of large-scale clustering of galaxies. We measure the power spectrum and the bispectrum of Sloan Digital Sky Survey galaxies and compare the result with predictions in an empirical model of modified gravity. Our model assumes an additional Yukawa-like term with two parameters that characterize the amplitude and the length scale of the modified gravity. The model predictions are calculated using two methods; second-order perturbation theory and direct N-body simulations. These methods allow us to study nonlinear evolution of large-scale structure. Using the simulation results, we find that perturbation theory provides reliable estimates for the power spectrum and the bispectrum in the modified Newtonian model. We also construct mock galaxy catalogs from the simulations, and derive constraints on the amplitude and the length scale of deviations from Newtonian gravity. The resulting constraints from the power spectrum are consistent with those obtained in our earlier, indicating the validity of the previous empirical modeling of gravitational nonlinearity in the modified Newtonian model. If linear biasing is adopted, the bispectrum of the Sloan Digital Sky Survey galaxies yields constraints very similar to those from the power spectrum. If we allow for the nonlinear biasing instead, we find that the ratio of the quadratic to linear biasing coefficients, b₂/b₁, should satisfy -0.25<b₂/b₁<0.19 for λ=5h^-1  Mpc and -0.19<b₂/b₁<0.13 for λ=10h^-1  Mpc in the modified Newtonian model.