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.

Revtex file, 21 pages, 4 figures available on request, accepted for publication on Phys. Rev. D