  The string effective action at tree level contains, in its bosonic sector,
the Einstein-Hilbert term, the dilaton, and the axion, besides scalar and gauge
fields coming from the Ramond-Ramond sector. The reduction to four dimensions
brings to scene moduli fields. We generalize this effective action by
introducing two arbitrary parameters, $\omega$ and $m$, connected with the
dilaton and axion couplings. In this way, more general frameworks can be
analyzed. Regular solutions with a bounce can be obtained for a range of
(negative) values of the parameter $\omega$ which, however, exclude the pure
string configuration ($\omega = - 1$). We study the evolution of scalar
perturbations in such cosmological scenarios. The predicted primordial power
spectrum decreases with the wavenumber with spectral index $n_s=-2$, in
contradiction with the results of the $WMAP$. Hence, all such effective string
motivated cosmological bouncing models seem to be ruled out, at least at the
tree level approximation.
