We find the spectrum $P\left(\omega \right)d\omega$ of the gravitational wave background produced in the early universe in string theory. We work in the framework of the recently discussed string driven cosmology, whose scale factors are computed with the low-energy effective string equations as well as self-consistent solutions of general relativity with a gas of strings as the source. The scale factor evolution is described by an early string driven inflationary stage with an instantaneous transition to a radiation-dominated stage and a successive matter-dominated stage. This is an expanding string cosmology evolution always running on positive proper cosmic time. The spectrum of the generated gravitons is computed in the framework of quantum field theory and in the appropiate effective string cosmology context. We study and show explicitly the effect of the dilaton field, characteristic to this kind of cosmology. We compute the spectrum for the same evolution description with three different approaches. Some features of gravitational wave spectra, such as peaks and asymptotic behaviors, are found to be a direct consequence of the dilaton involved in the string low-energy effective action and not only of the scale factor evolution. We make use of a careful treatment of the scale factor evolution and involved transitions. This allows us to compute a full prediction on the power spectrum of gravitational waves without any free parameters. A comparative analysis of different treatments, solutions, and compatibility with observational bounds or detection perspectives is made.

• Received 14 May 1999

DOI:https://doi.org/10.1103/PhysRevD.61.083515