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 $\phi$, at the scale with wavenumber mode $k$. In
the extreme case of instantaneous reheating $\phi_k$ 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.
