Topological Gravity Motivated by Renormalization Group

Taisaku Mori,Shin’Ichi Nojiri

doi:10.3390/sym10090396

Abstract

Recently, we have proposed models of topological field theory including gravity in Mod. Phys. Lett. A 2016, 31, 1650213 and Phys. Rev. D 2017, 96, 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. In particular, we construct a model with the solutions corresponding to the de Sitter space-time both in the ultraviolet and the infrared fixed points.

Highlights

We find λ − λ0 6= 0 in general because λ plays the role of the dynamical cosmological constant and BRS symmetry is spontaneously broken in general
The coupling constants are replaced by scalar fields, which run as in the renormalization group following the scale of the universe
We have constructed a model which connects the inflation in the early universe and the accelerating expansion of the present universe or late time

Summary

Introduction

Rev. D 2017, 96, 024009 [2], models of topological field theory including gravity have been proposed in order to solve the cosmological constant problem. Among of the possible scenarios, we have proposed the models of the topological field theory including gravity in [1] and the cosmology described by these models has been discussed in [2]. Motivated by the above observation, in this paper, we propose new models where there appear an infrared fixed point, which may correspond to the late time universe, and an ultraviolet fixed point, which may correspond to the early universe. The last section is devoted to the summary, where we mention on the problems which have not been solved in this paper and some possibilities to solve them are shown in Appendix A

Review of the Models of Topological Field Theory Including Gravity

Model Motivated by Renormalization Group

Summary