The Variational principle, Conformal and Disformal transformations, and the degrees of freedom

TL;DR

This paper explores how conformal and disformal transformations affect the degrees of freedom in modified gravity theories, especially in mimetic dark matter models, analyzing their variational principles and viability.

Contribution

It provides a detailed explanation of the variational principle underlying these transformations and discusses concerns regarding the viability of the resulting models.

Findings

Transformations can produce new mimetic solutions.

Dependence on scalar kinetic terms influences model properties.

Questions raised about the physical viability of these models.

Abstract

Conformal and disformal transformations are now being very intensively studied in the context of various modified gravity theories. In particular, some special classes of them can be used for constructing Mimetic Dark Matter models. Recently, it has been shown that many more transformations of this type, if not virtually all of them when the coefficients depend on the scalar kinetic term, can produce new solutions with mimetic properties. The aim of this paper is to explain how it works at the level of the variational principle, and to express some worries about viability of these models.