  We consider the dynamics of the open string tachyon condensation in a
framework of the cubic fermionic String Field Theory including a non-minimal
coupling with closed string massless modes, the graviton and the dilaton.
Coupling of the open string tachyon and the dilaton is motivated by the open
String Field Theory in a linear dilaton background and the flat space-time. We
note that the dilaton gravity provides several restrictions on the tachyon
condensation and show explicitly that the influence of the dilaton on the
tachyon condensation is essential and provides a significant effect:
oscillations of the Hubble parameter and the state parameter become of a
cosmological scale. We give an estimation for the period of these oscillations
(0.1-1) Gyr and note a good agreement of this period with the observed
oscillations with a period (0.15-0.65) Gyr in a distribution of quasar spectra.
