  We eliminate the parameters originally present in models of inflation of the
$\alpha$-attractor type in favor of the scalar spectral index $n_s$ and the
tensor-to-scalar ratio $r$. We then write expressions for the number of
$e$-folds during reheating $ N_ {re} $. By imposing reasonable conditions on
$N_{re}$ we can restrict $n_s$ and $r$ and in turn, we use these constraints in
order to find bounds for cosmological quantities of interest such as the number
of $e$-folds during inflation and the radiation dominated eras, as well as for
the reheating temperature and the running index. The minimum condition that $N_
{re}$ must satisfy is $N_ {re}\geq 0$ which we use to constrain the
cosmological quantities mentioned above. In particular, we find that the
tensor-to-scalar ratio $r$ (and as a consequence the energy scale of inflation)
is bounded from below. We provide figures illustrating the behavior of these
quantities as functions of $r$ for several values of $n_s$ and tables
containing the bounds so obtained.
