Phenomenology in type-I minimally modified gravity
  We study cosmology in a class of minimally modified gravity (MMG) with two
local gravitational degrees of freedom. We classify modified gravity theories
into type-I and type-II: theories of type-I have an Einstein frame and can be
recast by change of variables as general relativity (GR) with a non-minimal
matter coupling, while theories of type-II have no Einstein frame. Considering
a canonical transformation of the lapse, the 3-dimensional induced metric and
their conjugate momenta we generate type-I MMG. We then show that
phenomenological deviations from GR, such as the speed of gravitational waves
$c_T$ and the effective gravitational constant for scalar perturbations $G_{\rm
eff}$, are characterized by two functions of an auxiliary variable. We study
the phenomenology of several models all having $c_T=1$. We obtain a scenario
with $c_T=1$ in which the effective equation-of-state parameter of dark energy
is different from $-1$ even though the cosmic acceleration is caused by a bare
cosmological constant, and we find that it is possible to reconstruct the
theory on choosing a selected time-evolution for the effective dark energy
component.
