A generic form of a low-energy effective action of superstring theories with one-loop quantum corrections is well known. Based on this action we derive the complete perturbation equations and general analytic solutions in cosmological spacetime. Using the solutions we identify the conserved quantities characterizing the perturbations, the amplitude of the gravitational wave and the perturbed three-space curvature in the uniform-field gauge both in the large-scale limit, and the angular momentum of rotational perturbation are conserved independently of changing gravity sector. The implications for calculating perturbation spectra generated in the inflation era based on the string action are presented.

• Received 20 January 1999

DOI:https://doi.org/10.1103/PhysRevD.61.043511