# Modifications of Gravity Via Differential Transformations of Field Variables

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## Abstract

**:**

## 1. Introduction

## 2. Examples of Theories with Differential Field Transformations

#### 2.1. Mechanics

#### 2.2. Massive Scalar Field

#### 2.3. The Hilbert–Palatini Approach

## 3. Isometric Embeddings and Regge–Teitelboim Gravity

**tr**means trace of a square root of matrix with indices $\mu $ and $\alpha $ (see the discussion of the details of the matrix root usage in the description of gravity in [46]). It can be checked (see details in [45]; note that ${j}_{a}^{\mu}$ used in the present paper differs from the analogous quantity in [45] by a multiplier $\sqrt{-g}$) that EoM of such theory are Equations (34) and (35) and the inducedness condition in Equation (29).

## 4. Mimetic Gravity and Its Extensions

#### 4.1. Mimetic Gravity

#### 4.2. Disformal Transformations

## 5. Concluding Remarks

- Is it possible to attain an arbitrary value of the original variables by choosing new variables?
- Is it possible to attain an arbitrary value of the variations of original variables by choosing the variations of new variables?

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Sheykin, A.; Solovyev, D.; Sukhanov, V.; Paston, S.
Modifications of Gravity Via Differential Transformations of Field Variables. *Symmetry* **2020**, *12*, 240.
https://doi.org/10.3390/sym12020240

**AMA Style**

Sheykin A, Solovyev D, Sukhanov V, Paston S.
Modifications of Gravity Via Differential Transformations of Field Variables. *Symmetry*. 2020; 12(2):240.
https://doi.org/10.3390/sym12020240

**Chicago/Turabian Style**

Sheykin, Anton, Dmitry Solovyev, Vladimir Sukhanov, and Sergey Paston.
2020. "Modifications of Gravity Via Differential Transformations of Field Variables" *Symmetry* 12, no. 2: 240.
https://doi.org/10.3390/sym12020240