Precise determination of the inflationary epoch and constraints for reheating

We present a simple formula that allows to calculate the value of the inflaton field, denoted by $ϕ$, at the scale with wavenumber mode $k$. In the extreme case of instantaneous reheating $ϕ_k$ is calculated exactly and all inflationary observables and quantities of interest follow. This formula, together with the fact that the scale factor $a_p$ at the pivot scale wavenumber $k_p=0.05/Mpc$ lies in the radiation era, allows the development of a diagrammatic approach to study the evolution of the universe. This scheme is complementary to the usual analytical method and some interesting results, independent of the model of inflation, can be obtained. As a concrete application of the ideas developed here we discuss them with some detail using the Starobinsky model of inflation.

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