Solution to the problem of time

TL;DR

This paper proposes a novel solution to the problem of time in quantum gravity by promoting the cosmological constant to a Lagrange multiplier, enabling a unitary quantum evolution and addressing key issues like vacuum energy and eternal inflation.

Contribution

It introduces a new approach that treats the cosmological constant as a Lagrange multiplier, resulting in a functional Schrödinger equation for gravity and resolving the problem of time.

Findings

Provides a unitary quantum evolution framework for gravity.

Decouples vacuum energy from the cosmological constant problem.

Offers a natural foliation that addresses eternal inflation measure issues.

Abstract

Despite the ultraviolet problems with canonical quantum gravity, as an effective field theory its infrared phenomena should enjoy fully quantum mechanical unitary time evolution. Currently this is not possible, the impediment being what is known as the problem of time. Here, we provide a solution by promoting the cosmological constant $\Lambda$ to a Lagrange multiplier constraining the metric volume element to be manifestly a total derivative. Because $\Lambda$ appears linearly in the Hamiltonian constraint, it unitarily generates time evolution, yielding a functional Schroedinger equation for gravity. Two pleasant side effects of this construction are that vacuum energy is dissociated from the cosmological constant problem, much like in unimodular gravity, and the natural foliation provided by the time variable defines a sensible solution to the measure problem of eternal inflation.