  In spite of the growing observational evidence for dark matter and dark
energy in the universe, their physical nature is largely unknown. In fact,
several authors have proposed modifications of Newton's law of gravity at
cosmological scales to account for the apparent acceleration of the cosmic
expansion. Inspired by such suggestions, we attempt to constrain possible
deviations from Newtonian gravity by means of the clustering of SDSS (Sloan
Digital Sky Survey) galaxies. To be specific, we assume a simple modification
of Newton's law with an additional Yukawa-type term characterized by the
amplitude \alpha and the length scale \lambda. Adopting spatially-flat
universes dominated by cold dark matter and/or dark energy, we solve a linear
perturbation equation for the growth of density fluctuations. In particular, we
find an exact analytic solution for the Einstein -- de Sitter case. Following
the Peacock-Dodds prescription, we compute the nonlinear power spectra of mass
fluctuations, perform a statistical comparison with the SDSS galaxy data, and
derive constraints in the \alpha-\lambda plane; for instance, we obtain the
constraints of -0.5<\alpha <0.6 and -0.8<\alpha<0.9 (99.7% confidence level)
for \lambda=5h^{-1}Mpc and 10h^{-1}Mpc, respectively. We also discuss several
future possibilities for improving our analysis.
