# Using Cosmological Perturbation Theory to Distinguish between GR and Unimodular Gravity

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## Abstract

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## 1. Introduction

## 2. Background Cosmological Structure

#### 2.1. Friedmann Equations

#### 2.2. UG and GR Vacuum Cosmological Solutions

## 3. Perturbative Analysis

#### 3.1. The Perturbed Equations in the Gauge-Invariant Formalism

#### 3.2. Vacuum Case: Perturbations

#### 3.3. Introducing Matter Fields

## 4. Gauge-Invariant Perturbations with Matter

## 5. An Extension of UG: Including Scalar Fields

## 6. Unimodular $\mathit{f}\left(\mathit{R}\right)$ Class of Theories

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Fabris, J.C.; Alvarenga, M.H.; Velten, H.
Using Cosmological Perturbation Theory to Distinguish between GR and Unimodular Gravity. *Symmetry* **2023**, *15*, 1392.
https://doi.org/10.3390/sym15071392

**AMA Style**

Fabris JC, Alvarenga MH, Velten H.
Using Cosmological Perturbation Theory to Distinguish between GR and Unimodular Gravity. *Symmetry*. 2023; 15(7):1392.
https://doi.org/10.3390/sym15071392

**Chicago/Turabian Style**

Fabris, Júlio C., Marcelo H. Alvarenga, and Hermano Velten.
2023. "Using Cosmological Perturbation Theory to Distinguish between GR and Unimodular Gravity" *Symmetry* 15, no. 7: 1392.
https://doi.org/10.3390/sym15071392