sufficiently large in order not to destroy the standard cosmology of the present and early Universe. In particular, the values of M considered in Refs. [19, 20] are not high enough for this purpose, because M should not be smaller than the Hubble parameter H ( t ) during the N ∼ 60 last e-folds of inflation in the early Universe in order to avoid overproduction of relic scalarons, as well as to solve other cosmological problems. In fact, if we take M ≈ 3 × 10 13 GeV, the scalaron itself can act as an inflaton [6] and generate primordial scalar (adiabatic) and tensor perturbations [21, 22] with the amplitudes and slopes of their power spectra in agreement with all observational data available today. Note, however, that as shown in Ref. [18], such a ”unified” model describing both primordial DE driving inflation in the early Universe and present DE driving recent acceleration of the Universe in the scope of f ( R ) gravity leads to slightly different predictions for parameters of the primordial perturbation spectra, as compared to the purely inflationary model with λR$_{s}$ = 0, due to a change in the number of observable e-folds of inflation N caused by different evolution of the Universe during generation and heating of usual matter after inflation. Furthermore, in this unified model the term in the square brackets in (3) should be modified for | R | < R$_{0}$ in such a way as to ensure the fulfillment of the stability condition f ′′ ( R ) > 0 in this region, too. So, we take this value of M and assume that the evolution of the Universe is identical to that in the standard ΛCDM model at high redshifts without any relic scalaron oscillations. Then the R $^{2}$/ 6 M 2 term is totally negligible in the epoch we are concerned here. Therefore, we do not include its contribution below. We can express field equations derived from the action in the following Einsteinian form. (the sign conventions here are the same as in Ref. [14]). Working in the spatially flat Friedmann-Robertson-Walker (FRW) space-time with the scale factor a ( t ), we find where H is the Hubble parameter and ρ is the energy density of the material content which we assume to consist of non-relativistic matter. R µ ν − 1 2 δ µ $_{ν}$R = − 8 πG ( T µ ν ( m ) + T µ ν (DE) ) , (4) 8 πGT µ ν (DE) ≡ F ′ ( R ) R µ ν − 1 2 F ( R ) δ µ ν + ( ∇ $^{µ}$∇ ν − δ µ ν □ ) F ′ ( R ) , F ( R ) ≡ f ( R ) − R (5) where 3 H 2 = 8 πGρ − 3 F ′ H 2 + 1 2 ( F ′ R − F ) − 3 H ˙ F ′ , (6) 2 ˙ H = − 8 πGρ − 2 F ′ ˙ H − ¨ F ′ + H ˙ F ′ , (7) 4