  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.
