# Renormalizability of Alternative Theories of Gravity: Differences between Power Counting and Entropy Argument

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## Abstract

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## 1. Introduction

## 2. A Summary of Extended and Modified Theories of Gravity

## 3. Spherical Symmetry

#### 3.1. $f\left(R\right)$ Gravity

#### 3.2. $f\left(\mathcal{G}\right)$ Gravity

#### 3.3. $f\left(T\right)$ Teleparallel Gravity

#### 3.4. Horava–Lifshitz Gravity

## 4. Power-Counting Analysis

## 5. Renormalizability via the Bekenstein–Hawking Entropy Argument

#### 5.1. The $f\left(R\right)$ Case

#### 5.2. The $f\left(\mathcal{G}\right)$ Case

#### 5.3. The Teleparallel Case

#### 5.4. The Horava–Lifshitz Case

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Bajardi, F.; Bascone, F.; Capozziello, S.
Renormalizability of Alternative Theories of Gravity: Differences between Power Counting and Entropy Argument. *Universe* **2021**, *7*, 148.
https://doi.org/10.3390/universe7050148

**AMA Style**

Bajardi F, Bascone F, Capozziello S.
Renormalizability of Alternative Theories of Gravity: Differences between Power Counting and Entropy Argument. *Universe*. 2021; 7(5):148.
https://doi.org/10.3390/universe7050148

**Chicago/Turabian Style**

Bajardi, Francesco, Francesco Bascone, and Salvatore Capozziello.
2021. "Renormalizability of Alternative Theories of Gravity: Differences between Power Counting and Entropy Argument" *Universe* 7, no. 5: 148.
https://doi.org/10.3390/universe7050148