Dark matter and dark energy as effects of modified gravity

We explain the e. ect of dark matter (flat rotation curve) using modified gravitational dynamics. We investigate in this context a low energy limit of generalized general relativity with a nonlinear Lagrangian L proportional to R-n, where R is the (generalized) Ricci scalar and n is parameter estimated from SNIa data. We estimate parameter beta in modified gravitational potential V (r) proportional to -1/r (1 + (r/r(c))beta). Then we compare value of beta obtained from SNIa data with beta parameter evaluated from the best fitted rotation curve. We. find beta similar or equal to 0.7 which becomes in good agreement with an observation of spiral galaxies rotation curve. We also. find preferred value of Omega(m),o from the combined analysis of supernovae data and baryon oscillation peak. We argue that although amount of dark energy (of non-substantial origin) is consistent with SNIa data and. at curves of spiral galaxies are reproduces in the framework of modi. fied Einstein's equation we still need substantial dark matter. For comparison predictions of the model with predictions of the ACDM concordance model we apply the Akaike and Bayesian information criteria of model selection.