The quantization of unimodular gravity and the cosmological constant problem

TL;DR

This paper presents a quantization approach for unimodular gravity that naturally suppresses quantum contributions to the cosmological constant, addressing both the first and second cosmological constant problems.

Contribution

It introduces a quantum effective action for unimodular gravity that prevents certain energy-momentum contributions from curving spacetime, offering a novel solution to the cosmological constant problems.

Findings

Quantum corrections do not source curvature in unimodular gravity.

The approach addresses the smallness of the observed cosmological constant.

A path integral formulation for unimodular gravity is constructed.

Abstract

A quantization of unimodular gravity is described, which results in a quantum effective action which is also unimodular, ie a function of a metric with fixed determinant. A consequence is that contributions to the energy momentum tensor of the form of the metric times a spacetime constant, whether classical or quantum, are not sources of curvature in the equations of motion derived from the quantum effective action. This solves the first cosmological constant problem, which is suppressing the enormous contributions to the cosmological constant coming from quantum corrections. We discuss several forms of uniodular gravity and put two of them, including one proposed by Henneaux and Teitelboim, in constrained Hamiltonian form. The path integral is constructed from the latter. Furthermore, the second cosmological constant problem, which is why the measured value is so small, is also addressed by this theory. We argue that a mechanism first proposed by Ng and van Dam for suppressing the cosmological constant by quantum effects obtains at the semiclassical level.