  The modified gravity with $f(R)=R^{1+\epsilon}$ ($\epsilon>0$) allows a
scaling solution where the density of gravity sector follows the density of the
dominant fluid. We present initial conditions of background and perturbation
variables during the scaling evolution regime in the modified gravity. As a
possible dark energy model we consider a gravity with a form
$f(R)=R^{1+\epsilon}+qR^{-n}$ ($-1<n \le 0$) where the second term drives the
late-time acceleration. We show that our $f(R)$ gravity parameters are very
sensitive to the baryon perturbation growth and baryon density power spectrum,
and present observational constraints on the model parameters. Our analysis
suggests that only the parameter space extremely close to the
$\Lambda\textrm{CDM}$ model is allowed.
