We compute the string energy-momentum tensor and 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 ) Unstable for R \to \infty with growing energy density \rho \sim R ^ { 2 - D } , negative pressure , and \gamma = ( D - 2 ) / ( D - 1 ) ; ( ii ) Dual for R \to 0 , with \rho \sim R ^ { - D } , positive pressure and \gamma = D / ( D - 1 ) ( as radiation ) ; ( iii ) Stable for R \to \infty with \rho \sim R ^ { 1 - D } , 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 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 .