# Topological Gravity Motivated by Renormalization Group

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## Abstract

**:**

**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.

## 1. Introduction

**2016**, 31, 1650213 [1] and Phys. Rev. D

**2017**, 96, 024009 [2], models of topological field theory including gravity have been proposed in order to solve the cosmological constant problem. The accelerating expansion of the present universe may be generated by the small cosmological constant. Although the cosmological constant could be identified with a vacuum energy, the vacuum energy receives very large quantum corrections from matters and therefore in order to obtain a realistic very small vacuum energy, very fine-tuning of the counter term for the vacuum energy is necessary (The discussion about the small but non-vanishing vacuum energy is given in [3], for example.) Motivated by this problem of large quantum corrections to the vacuum energy, models of unimodular gravity [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30] have been proposed. There have been also proposed many scenarios, such as the sequestering mechanism [31,32,33,34,35,36,37,38]. 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].

## 2. Review of the Models of Topological Field Theory Including Gravity

## 3. Model Motivated by Renormalization Group

## 4. Summary

- Because the shift symmetry as in (8) is lost, the models in this paper do not solve the problem of the large quantum correction.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Some Propositions to Improve the Models

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**MDPI and ACS Style**

Mori, T.; Nojiri, S.
Topological Gravity Motivated by Renormalization Group. *Symmetry* **2018**, *10*, 396.
https://doi.org/10.3390/sym10090396

**AMA Style**

Mori T, Nojiri S.
Topological Gravity Motivated by Renormalization Group. *Symmetry*. 2018; 10(9):396.
https://doi.org/10.3390/sym10090396

**Chicago/Turabian Style**

Mori, Taisaku, and Shin’ichi Nojiri.
2018. "Topological Gravity Motivated by Renormalization Group" *Symmetry* 10, no. 9: 396.
https://doi.org/10.3390/sym10090396