The dilaton field is an essential component of all superstring models, and thus of the cosmological scenarios based on the string effective action. In particular, as shown in the previous chapters, the dilaton may control the inflationary dynamics and play a fundamental role in the generation of the primordial spectra of quantum fluctuations amplified by inflation. Also, it is the dilaton which controls the intensity of the various coupling strengths, and which may drive the Universe towards a phase of strong coupling possibly preceding the standard decelerated evolution. Thus, we can say that the dilaton (together with the other moduli fields, associated with the dynamics of the extra dimensions) is one of the most typical ingredients of models of string cosmology inflation, and is the basis of the main differences between the string models and the standard inflationary models based on the general relativistic equations.

In the post-inflationary epochs we may expect that the dilaton, like the other moduli fields, tends to approach a stabilized configuration either under the action of an appropriate potential (attracting it to a local minimum), or simply as a consequence of the standard, radiation-dominated dynamics: the low-energy string cosmology equations admit in fact asymptotic, radiation-dominated solutions at constant dilaton (see Eq. (4.58), and the discussion of Section 6.2).