  Following a suggestion by Gasperini and Veneziano, that String Cosmology can
be reconciled with Inflation and, hence, with the Standard Big Bang, we display
an analytical solution which possesses four interesting properties: (1) it is
non-singular; (2) it distinguishes the dynamics of the external scale factor,
$a(t)$, from that of the internal one, $b(t)$; (3) it exhibits a non-monotonic
behavior of $a(t)$; and (4) it stabilizes both Newton's constant and $b(t)$
(the latter to a finite, non-vanishing value). The interest of the
non-monotonic evolution of $a(t)$ consists in the fact that it contains three
phases of accelerated expansion, contraction and expansion before the final
decelerated expansion which eventually becomes the Standard Big Bang. The total
number of e-folds of the three accelerated eras can be calculated and tuned to
fit the requests of observational astronomy.
