Time-dependent flux backgrounds in type IIB supergravity

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.