Cosmological solutions in low-energy effective field theory for type IIA superstrings

Abstract

It is known that to obtain cosmological solutions consistent with the Hubble law and accelerated expansion, it is necessary to represent space-time in the form of de Sitter space of the first kind, which ismost simply described by a Robertson-Walkermetric having the scale factor with exponential time dependence. In standard general relativity, this solution is obtained by introduction of the cosmological constant Λ associated with dark energy, whose nature is still not clear. It would be of some interest to consider theories allowing one to obtain cosmological-type solutions without using an effective Λ term. This role was at their time claimed by various supergravity theories which are low-energy approximations of superstring theories. However, it was found that in these theories there are so-called no-go theorems which do not allow solutions in the form of de Sitter space of the first kind. It turned out that this problem can be solved in at least two ways. The first way is to admit the possibility of extra time dimensions, as was demonstrated for the ten-dimensional supergravity by Arefyeva et al. Another way is to consider corrections of higher order in the curvature tensor, which is a subject of this paper. As is known, non-chiral ten-dimensional N = 2 supergravity is a low-energy approximation of type IIA superstring theory. In the present paper, we consider the effective action for type IIA superstring theory, taking into account fourthorder curvature corrections. It is shown that in this case, indeed, one can obtain a cosmological solution in the form of de Sitter space, describing an exponential expansion of space without an effective Λ term.