Multidimensional Cosmology with a Generalized Maxwell Field: Integrable Cases

TL;DR

This paper explores integrable multidimensional cosmological models with a generalized Maxwell field, revealing solutions with perfect fluids and scalar fields in even-dimensional spacetimes, including flat and non-flat geometries.

Contribution

It introduces new integrable cases of multidimensional cosmologies with a generalized Maxwell field, including models with perfect fluids and scalar fields, expanding the understanding of such systems.

Findings

Identified integrable vacuum and perfect fluid models with a generalized Maxwell field.

Derived families of spatially flat and non-flat cosmological solutions.

Showed inclusion of scalar fields or ultrastiff fluids in these models.

Abstract

We consider multidimensional cosmologies in even-dimensional space-times (D=2n) containg perfect fluid and a multidimensional generalization of the Maxwell field, preserving its conformal invariance (the F field, an n-form). Among models with an isotropic physical 3-space some integrable cases are found: vacuum models (which are integrable in the general case) and some perfect fluid models with barotropic equations of state. All of them contain a component of the F field appearing as an additional scalar in 4 dimensions. A two-parameter family of spatially flat models and four one-parameter families, including non-spatially flat models, have been obtained (where the parameters are constants from the fluid equation of state). All these integrable models admit the inclusion of a massless scalar field or an additional fluid with ultrastiff equation of state. Basic properties of vacuum models in the physical conformal frame are outlined.