  We compute the string energy-momentum tensor and {\bf derive} the string
equation of state from exact string dynamics in cosmological spacetimes.
$1+1,~2+1$ and $D$-dimensional universes are treated for any expansion factor
$R$. Strings obey the perfect fluid relation $ p = (\gamma -1) \rho $ with
three different behaviours: (i) {\it Unstable} for $ R \to \infty $ with
growing energy density $ \rho \sim R^{2-D} $, {\bf negative} pressure, and $
\gamma =(D-2)/(D-1) $; (ii){\it Dual} for $ R \to 0 $, with $ \rho \sim R^{-D}
$, {\bf positive} pressure and $\gamma = D/(D-1) $ (as radiation); (iii) {\it
Stable} for $ R \to \infty $ with $ \rho \sim R^{1-D} $, {\bf vanishing}
pressure and $\gamma = 1 $ (as cold matter). We find the back reaction effect
of these strings on the spacetime and we take into account the quantum string
decay through string splitting. This is achieved by considering {\bf
self-consistently} the strings as matter sources for the Einstein equations, as
well as for the complete effective string equations. String splitting
exponentially suppress the density of unstable strings for large $R$. The
self-consistent solution to the Einstein equations for string dominated
universes exhibits the realistic matter dominated behaviour $ R \sim
(X^0)^{2/(D-1)}\; $ for large times and the radiation dominated behaviour $ R
\sim (X^0)^{2/D}\; $ for early times. De Sitter universe does not emerge as
solution of the effective string equations. The effective string action
(whatever be the dilaton, its potential and the central charge term) is not the
appropriate framework in which to address the question of string driven
inflation.
