We explain the effect 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 { \cal L } \propto 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 ) \propto - \frac { 1 } { r } ( 1 + ( \frac { 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 \simeq 0.7 which becomes in good agreement with an observation of spiral galaxies rotation curve .
We also find preferred value of \Omega _ { m, 0 } 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 flat curves of spiral galaxies are reproduces in the framework of modified Einstein ’ s equation we still need substantial dark matter .
For comparison predictions of the model with predictions of the \Lambda CDM concordance model we apply the Akaike and Bayesian information criteria of model selection .