O(d,d) covariant cosmology in isotropic and anisotropic spaces

In this thesis we analyse the O(d,d) covariant cosmological theory presented by Hohm and Zwiebach motivated by the quest for de Sitter solutions in the Einstein 4-dimensional frame. For this purpose, we develop the theory for an anisotropic metric and search for the fixed points of the dynamical system in the string frame, later translating these stable solutions into the Einstein frame, we find Minkowski and exact de Sitter solutions as well as another family of solutions that can be constrained to have an accelerated expansion and a positive Hubble parameter asymptotically decreasing towards zero. These constraints establish possible intervals for our physical degrees of freedom. Finally, we perform the compactification of the action with all the α′ corrections, encoded in the F function, for our anisotropic theory. Therefore, we have the possibility to examine the shape of the F function with all its corrections in the Einstein frame. We obtain an Einstein-Hilbert action minimally coupled to two scalars at order zero in α′, and a perturbative potential given by F in this new frame which no longer depends only on the Hubble parameter, but mixes all the degrees of freedom of our action.