Unimodular gravity, was originally suggested long time ago as a possible
mechanism of explaining the cosmological constant problem. In the
standard formulation of the theory, it is known that the unimodularity
condition restricts the gauge symmetries of the gravitational action to
a subset of the full diffeomorphisms, as well as that the classical
dynamics of the theory are the same as those of standard General
Relativity (GR). The quantum equivalence of the two theories, however,
has not been well studied so far.
In this talk, I will discuss the classical and quantum dynamics of
unimodular gravity, based on a unimodular formulation of GR which enjoys
full diffeomorphism symmetry by construction. I will first explain how
the classical dynamics of the theory match exactly those of GR, and how
the cosmological constant problem expresses itself in this context. I
will proceed with presenting the key quantum properties of the theory in
the context of the Exact Renormalisation Group, explaining how
(in)equivalence with GR is established, and discussing some new features
which emerge in this context.