Topological Gravity motivated by Renormalization Group

TL;DR

This paper introduces new topological gravity models inspired by renormalization group ideas, featuring fixed points that could describe different universe epochs, and constructs solutions resembling de Sitter space at these fixed points.

Contribution

It proposes novel topological gravity models with fixed points, extending previous models to include infrared and ultraviolet behaviors relevant to cosmology.

Findings

Models exhibit scale-dependent coupling constants similar to renormalization group flow.

Constructed solutions correspond to de Sitter space at fixed points.

Models potentially describe early and late universe dynamics.

Abstract

Recently we have proposed models of topological field theory including gravity in Mod. Phys. Lett. A 31 (2016) no.37, 1650213 and Phys. Rev. D 96 (2017) no.2, 024009, in order to solve the problem of the cosmological constant. The Lagrangian densities of the models are BRS (Becchi-Rouet-Stora) exact and therefore the models can be regarded as topological theories. In the models, the coupling constants, including the cosmological constant, look as if they run with the scale of the universe and its behavior is very similar to the renormalization group. Motivated by these models, we propose new models with an the infrared fixed point, which may correspond to the late time universe, and an ultraviolet fixed point, which may correspond to the early universe. Especially we construct a model with the solutions corresponding to the de Sitter space-time both in the ultraviolet and the infrared fixed points.