Unimodular-Mimetic Cosmology
  We combine the unimodular gravity and mimetic gravity theories into a unified
theoretical framework, which is proposed to provide a suggestive proposal for a
framework that may assist in the discussion and solution search of the
cosmological constant problem and of the dark matter issue. After providing the
formulation of the unimodular mimetic gravity and investigating all the new
features that the vacuum unimodular gravity implies, by using the underlying
reconstruction method, we realize some well known cosmological evolutions, with
some of these being exotic for the ordinary Einstein-Hilbert gravity.
Specifically we provide the vacuum unimodular mimetic gravity description of
the de Sitter cosmology and of the perfect fluid with constant equation of
state cosmology. As we demonstrate, these cosmologies can be realized by vacuum
mimetic unimodular gravity, without the existence of any matter fluid source.
Moreover, we investigate how cosmologically viable cosmologies, which are
compatible with the recent observational data, can be realized by the vacuum
unimodular mimetic gravity. Since in some cases, the graceful exit from
inflation problem might exist, we provide a qualitative description of the
mechanism that can potentially generate the graceful exit from inflation in
these theories, by searching for the unstable de Sitter solutions in the
context of unimodular mimetic theories of gravity.
