Higher-dimensional models in gravitational theories of quarticLagrangians

TL;DR

This paper investigates ten-dimensional gravitational models with quartic curvature terms, revealing exponential and power-law solutions, and identifying attractor states corresponding to inflationary external space and contracting internal space.

Contribution

It introduces a detailed analysis of higher-dimensional quartic Lagrangian models, demonstrating the existence of attractor solutions with inflationary external and contracting internal dimensions.

Findings

Existence of exponential and power-law solutions in ten-dimensional models.

Identification of attractor points corresponding to extended De Sitter spacetimes.

External space undergoes inflation while internal space contracts.

Abstract

Ten-dimensional models, arising from a gravitational action which includes terms up to the fourth order in curvature tensor, are discussed. The spacetime consists of one timelike dimension and two maximally symmetric subspaces, filled with matter in the form of an anisotropic fluid. Numerical integration of the cosmological field equations indicates that exponential, as well as power law, solutions are possible. We carry out a dynamical study of the results in the H_{ext} - H_{int} plane and confirm the existence of "attractors" in the evolution of the Universe. Those attracting points correspond to "extended De Sitter" spacetimes, in which the external space exhibits inflationary expansion, while the internal one contracts.