Disformal Gravity Theories: A Jordan Frame Analysis
  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.
