Diffusion in unimodular gravity: Analytical solutions, late-time
  acceleration, and cosmological constraints
  Unimodular gravity is an appealing approach to address the cosmological
constant problem. In this scenario, the vacuum energy density of quantum fields
does not gravitate and the cosmological constant appears merely as an
integration constant. Recently, it has been shown that energy diffusion that
may arise in quantum gravity and in theories with spontaneous collapse is
compatible with this framework by virtue of its restricted diffeomorphism
invariance. New studies suggest that this phenomenon could lead to higher-order
equations in the context of homogeneous and isotropic Universe, affecting the
well-posedness of their Cauchy initial-value problem. In this work, we show
that this issue can be circumvented by assuming an equation of state that
relates the energy density to the function that characterizes the diffusion. As
an application, we solve the field equations analytically for an isotropic and
homogeneous Universes in a barotropic model and in the mass-proportional
continuous spontaneous localization (CSL) scenario, assuming that only dark
matter develops energy diffusion. Different solutions possessing phase
transition from decelerated to accelerated expansion are found. We use
cosmological data of type Ia Supernovae and observational Hubble data to
constrain the free parameters of both models. It is found that very small but
nontrivial energy nonconservation is compatible with the barotropic model.
However, for the CSL model, we find that the best-fit values are not compatible
with previous laboratory experiments. We comment on this fact and propose
future directions to explore energy diffusion in cosmology.
