Universal accelerating cosmologies from 10d supergravity

Abstract

We study 4d Friedmann-Lemaître-Robertson-Walker cosmologies obtained from time-dependent compactifications of Type IIA 10d supergravity on various classes of 6d manifolds (Calabi-Yau, Einstein, Einstein-Kähler). The cosmologies we present are universal in that they do not depend on the detailed features of the compactification manifold, but only on the properties which are common to all the manifolds belonging to that class. Once the equations of motion are rewritten as an appropriate dynamical system, the existence of solutions featuring a phase of accelerated expansion is made manifest. The fixed points of this dynamical system, as well as the trajectories on the boundary of the phase space, correspond to analytic solutions which we determine explicitly. Furthermore, some of the resulting cosmologies exhibit eternal or semi-eternal acceleration, whereas others allow for a parametric control on the number of e-foldings. At future infinity, one can achieve both large volume and weak string coupling. Moreover, we find several smooth accelerating cosmologies without Big Bang singularities: the universe is contracting in the cosmological past ($T<0$), expanding in the future ($T>0$), while in the vicinity of $T=0$ it becomes de Sitter in hyperbolic slicing. We also obtain several cosmologies featuring an infinite number of cycles of alternating periods of accelerated and decelerated expansions.

v1: 38 pages + appendices, 18 figures; v2-v4: minor modifications and corrected typos

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