On One Model of the Geometrical Quintessence

A cosmological model with modification of the Einstein-Hilbert action by the correction $f(R)\propto \beta R^n$ is considered. Such way of the description of the ``geometrical'' dark energy has been introduced repeatedly and the coefficients of the model were chosen to be fit against some observational data. In this paper the unambiguous choice of parameters $n$ and $\beta$ is proposed from the follow reasons: the exponent $n$ close to 1.2953 follows from the request for the evolution of the Universe after recombination to be close to the evolution of the flat FRW model with cold dark matter and the reasonable age of the Universe defines the magnitude of the coefficient $\beta$. Such a model corresponding to the evolution of the Universe with the dynamical $\Lambda$-term describes well enough the observational data.