Precise determination of the inflationary epoch and constraints for reheating

Gabriel German

Published 2020-02-25Version 1

We present a simple formula which allows to calculate the value of the inflaton field, denoted by $\phi$, at the scale $k$. From here all inflationary observables follow. We illustrate the procedure with Starobinsky model of inflation. This gives an spectral index $n_s=0.96534$ with running $\alpha=-6.1 \times 10^{-4}$, tensor-to-scalar ratio $r=0.0034$ within reach of future experiments and an inflationary energy scale of $7.8 \times 10^{15}GeV$. We also discuss the reheating epoch finding a constraint equation for the effective number of degrees of freedom $g_{re}$. This constraint translates into constraints for the reheating temperature at the end of the reheating era $T_{re}$ and for the number of e-folds during reheating and also during matter domination. For the Starobinsky model we find that $g_{re} \lesssim 83$ giving a bound $T_{re}\lesssim 80\,GeV$ with $40.2 > N_{re} > 31.2$ and $17.4 < N_{rd} < 26.4$ for the number of e-folds during reheating and during radiation domination, respectively.