Higher-dimensional models in gravitational theories of quartic Lagrangians

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 time direction 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.

Accelerating Cosmologies and Inflation From M/Superstring Theories

“…A tiny perturbation to the exact solution is found to lead to interesting behavior of an accelerating phase. Consider a small perturbation around the solution (76). Let…”

“…The higher-order curvature terms called Lovelock gravity 73 were also considered in higher-dimensional cosmology. 74,75,76 The lowest higher order corrections are expected to appear in this form called Gauss-Bonnet (GB) terms which are the special combination without ghosts. 77 In fact, it is known that this combination appears in the low-energy effective theories of heterotic strings, 78,79 and extensive study of these theories was carried out.…”