Model independent results for the inflationary epoch and the breaking of the degeneracy of models of inflation

Abstract

We address the problem of determining inflationary characteristics in a model independent way. We start from a recently proposed equation which allows to accurately calculate the value of the inflaton at horizon crossing ϕk. We then use an equivalent form of this equation to write a formula that relates the number of e-folds from horizon crossing to the pivot scale Nke+Nep with the tensor-to-scalar index r, hence a general bound for Nke+Nep follows. Nke is the number of e-folds from the scale factor ak during inflation to the end of inflation at ae and Nep is the number of e-folds from ae to the pivot scale factor ap. In particular, at present r < 0.063 implies Nke+Nep< 112.5 e-folds at k=kp and 128.1 e-folds at the present scale with wavenumber mode k0. We also give a lower bound to the size of the universe during the inflationary epoch that gave rise to the current observable universe. We also discussed the problem of degeneracy of inflationary models and argue that this degeneration can only be resolved by studying model predictions from the reheating epoch.