Disformal Gravity Theories: A Jordan Frame Analysis

TL;DR

This paper introduces the Jordan frame formulation for disformal gravity theories, analyzes their cosmological implications, and finds that disformal effects are often negligible or lead to phantom dark energy behavior.

Contribution

It provides the first detailed Jordan frame analysis of disformal theories, clarifying their late-time cosmology and resolving issues associated with the Einstein frame.

Findings

Disformal effects are often irrelevant in late-time cosmology.

The universe can evolve towards a phantom phase with equation of state -3.

De-Sitter solutions exist in certain parameter regimes.

Abstract

The Jordan frame action for general disformal theories is presented and studied for the first time, motivated by several unresolved mysteries that arise when working in the Einstein frame. We present the Friedmann equations and, specialising to exponential functions, study the late-time cosmology using dynamical systems methods and by finding approximate solutions. Our analysis reveals that either the disformal effects are irrelevant or the universe evolves towards a phantom phase where the equation of state of dark energy is $-3$. There is a marginal case where the asymptotic state of the universe depends on the model parameters and de-Sitter solutions can be obtained. Our findings indicate that the metric singularity found using the Einstein frame construction corresponds phantom behaviour in the Jordan frame and we argue that this is the case for general disformal theories.