Falsifying Tree Level String Motivated Bouncing Cosmologies

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.