Quantum mechanics

Theoretical physics

Spacetime

Pure mathematics

Mathematical physics

f(R) gravity

Quantum gravity

Diffeomorphism

Physics

Scalar (mathematics)

Mathematics

Geometry

Quantum

Unimodular matrix

General relativity

Path integral formulation

Journal of High Energy Physics

A bstract We formally prove the existence of a quantization procedure that makes the path integral of a general diffeomorphism-invariant theory of gravity, with fixed total spacetime volume, equivalent to that of its unimodular version. This is achieved by means of a partial gauge fixing of diffeomorphisms together with a careful definition of the unimodular measure. The statement holds also in the presence of matter. As an explicit example, we consider scalar-tensor theories and compute the corresponding logarithmic divergences in both settings. In spite of significant differences in the coupling of the scalar field to gravity, the results are equivalent for all couplings, including non-minimal ones.

Can quantum fluctuations differentiate between standard and unimodular gravity?