Time-dependent flux backgrounds in type IIB supergravity

TL;DR

This paper constructs explicit time-dependent type IIB supergravity backgrounds with fluxes and internal Calabi-Yau spaces, satisfying energy conditions and potentially applicable to early universe cosmology.

Contribution

It provides new analytic solutions with time-dependent metrics and fluxes in type IIB supergravity, extending previous no-go theorems and including noncompact scale factors.

Findings

Solutions satisfy all classical energy conditions.

Four-dimensional Ricci scalar is negative in explicit examples.

Generalizations suggest positive Ricci scalar backgrounds are possible.

Abstract

We analytically construct families of type IIB supergravity backgrounds in ten dimensions in which the four-dimensional metric is time dependent, while the six-dimensional internal space is an arbitrary compact Calabi-Yau manifold (with no restriction on holonomy) up to an overall time-dependent scale factor. Our solutions include cases with all fluxes (three-form and self-dual five-form) switched on, as well as cases with subsets of these fluxes, together with a time-dependent axiodilaton in most cases. These constructions require no local sources. We show that the associated energy-momentum tensors (both 10D and the resulting 4D effective) satisfy the null, weak, strong, and dominant energy conditions. In our explicit constructions, the Ricci scalar of the four-dimensional Einstein frame metric is negative; such backgrounds may find applications to anisotropic or FLRW cosmologies in the early universe. We also revisit the Maldacena--Nu\~nez no-go analysis, incorporating new elements that appear in our constructions, namely an overall noncompact spacetime-dependent scale factor multiplying the internal metric, and field strengths with components partially covering the noncompact directions. We argue that, with these generalizations, a four-dimensional Einstein-frame metric with positive Ricci scalar cannot be ruled out by such an analysis.