Novel matter coupling in general relativity via canonical transformation
  We study canonical transformations of general relativity (GR) to provide a
novel matter coupling to gravity. Although the transformed theory is equivalent
to GR in vacuum, the equivalence no longer holds if a matter field minimally
couples to the canonically transformed gravitational field. We find that a
naive matter coupling to the transformed field leads to the appearance of an
extra mode in the phase space, rendering the theory inconsistent. We then find
a consistent and novel way of matter coupling: after imposing a gauge fixing
condition, a matter field can minimally couple to gravity without generating an
unwanted extra mode. As a result, the way matter field couples to the
gravitational field determines the preferred time direction and the resultant
theory has only two gravitational degrees of freedom. We also discuss the
cosmological solution and linear perturbations around it, and confirm that
their dynamics indeed differ from those in GR. The novel matter coupling can be
used for a new framework of modified gravity theories.
