General Relativity With An Auxiliary Dimension

TL;DR

This paper extends General Relativity with an auxiliary dimension, leading to a selfaccelerated solution that explains cosmic acceleration as a geometric effect, with stable perturbations and positive Hamiltonian in certain conditions.

Contribution

It introduces a novel extension of GR with an auxiliary dimension, resulting in a selfaccelerated universe solution independent of the cosmological constant.

Findings

Selfaccelerated solution mimics cosmic acceleration

Perturbations include ghost-free massless or massive gravitons

Hamiltonian is positive for the selfaccelerated solution

Abstract

I consider an extension of General Relativity by an auxiliary non-dynamical dimension that enables our space-time to acquire an extrinsic curvature. Obtained gravitational equations, without or with a cosmological constant, have a selfaccelerated solution that is independent of the value of the cosmological constant, and can describe the cosmic speedup of the Universe as a geometric effect. Background evolution of the selfaccelerated solution is identical to that of ordinary de Sitter space. I show that linear perturbations on this solution describe either a massless graviton, or a massive graviton and a scalar, which are free of ghosts and tachyons for certain choices of boundary conditions. The obtained linearized expressions suggest that nonlinear interactions should, for certain boundary conditions, be strongly coupled, although this issue is not studied here. The full nonlinear Hamiltonian of the theory is shown to be positive for the selfaccelerated solution, while in general, it reduces to surface terms in our and auxiliary dimensions.