Model independent results for the inflationary epoch and the breaking of
  the degeneracy of models of inflation
  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 $\phi_k$. 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 $N_{ke}+N_{ep}$
with the tensor-to-scalar index $r$, hence a general bound for $N_{ke}+N_{ep}$
follows. $N_{ke}$ is the number of e-folds from the scale factor $a_k$ during
inflation to the end of inflation at $a_e$ and $N_{ep}$ is the number of
e-folds from $a_e$ to the pivot scale factor $a_p$. In particular, at present
$r < 0.063$ implies $N_{ke}+N_{ep}< 112.5$ e-folds at $k=k_p$ and 128.1 e-folds
at the present scale with wavenumber mode $k_0$. 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.
