Geometric Model of Quintessence

On basis of modification of Einstein's gravitational equations by adding the term $f(R)\propto \beta R^n$, a geometric model of quintessence is proposed. The evolution equation for the scale factor $a$ of the Universe is analyzed for the two parameters $n=2$ and $n=4/3$, which were preferred by previous studies of the early Universe. Another choice of parameters $n$ and $\beta$ is proposed from the following 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 reasonable age of the Universe defines the value 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.