Accelerated Cosmological Models in Modified Gravity tested by distant   Supernovae SNIa data
  Recent supernovae of type Ia measurements and other astronomical observations suggest that our universe is in accelerating phase of evolution at the present epoch. While a dark energy of unknown form is usually proposed as the most feasible mechanism for the acceleration, there are appears some alternative conception that some effects arising from generalization of Einstein equation can mimic dark energy through a modified Friedmann equation. In this work we investigate some observational constraints on modified Friedmann equation obtained from generalized Lagrangian ${\cal L} \propto R^n$ in minimal coupling with matter in Palatini formalism. We mainly concentrate on the constraints of model parameters from distant supernovae but other constraint from baryon oscillation prior is also considered. We obtain the confidence levels on two additional model parameter ($n$,$\Omega_{m,0}$). We conclude that the FRW model of First-Order Non-linear gravity survives several observational test like SNIa observation and baryon oscillation peaks. We find preferred value of $\Omega_{m,0} \simeq 0.3$ from combined analysis of supernovae data and baryon oscillation peak. For deeper statistical analysis we apply Akaike and Bayesian information criteria of model selection for comparison prediction of the model with prediction of concordance $\Lambda$CDM model. 
Andrzej Borowiec, Wlodzimierz Godlowski, Marek Szydlowski