  Unimodular gravity is classically equivalent to General Relativity. This
equivalence extends to actions which are functions of the curvature scalar. At
the quantum level, the dynamics could differ. Most importantly, the
cosmological constant is not a coupling in the unimodular action, providing a
new vantage point from which to address the cosmological constant fine-tuning
problem. Here, a quantum theory based on the asymptotic safety scenario is
studied, and evidence for an interacting fixed point in unimodular f(R) gravity
is found. We study the fixed point and its properties, and also discuss the
compatibility of unimodular asymptotic safety with dynamical matter, finding
evidence for its compatibility with the matter degrees of freedom of the
Standard Model.
