Abstract
We discuss unimodular gravity at a classical level, and in terms of its extension into the UV through an appropriate path integral representation. Classically, unimodular gravity is simply a gauge fixed version of General Relativity (GR), and as such it yields identical dynamics and physical predictions. We clarify this and explain why there is no sense in which it can "bring a new perspective" to the cosmological constant problem. The quantum equivalence between unimodular gravity and GR is more of a subtle question, but we present an argument that suggests one can always maintain the equivalence up to arbitrarily high momenta. As a corollary to this, we argue that whenever inequivalence is seen at the quantum level, that just means we have defined two different quantum theories that happen to share a classical limit.
Highlights
When Einstein laid down the foundations for general relativity (GR) [1], he remarked that the laws of gravity sometimes took on a simpler form in certain coordinate systems, and illustrated his point by choosing so-called unimodular coordinates, where det gμν = −1
This choice of coordinates yields the same predictions as any other in a diffeomorphism invariant theory – a seemingly obvious fact that is at the heart of the equivalence between classical GR and so-called unimodular gravity
In the canonical approach to quantum gravity, it has been suggested that unimodular gravity can help address the problem of time [9,10], such a claim has been strongly refuted [11]
Summary
When Einstein laid down the foundations for GR [1], he remarked that the laws of gravity sometimes took on a simpler form in certain coordinate systems, and illustrated his point by choosing so-called unimodular coordinates, where det gμν = −1 This choice of coordinates yields the same predictions as any other in a diffeomorphism invariant theory – a seemingly obvious fact that is at the heart of the equivalence between classical GR and so-called unimodular gravity. One might imagine taking the path integral for GR and first dividing out the longitudinal diffeomorphsims satisfying ∇μξ μ = 0, such as to give us the path integral for unimodular gravity This is essentially the spirit behind the claims made in Ref. This means that the equivalence can always be broken at the quantum level by allowing the additional fields to exist as external legs in Feynman diagrams
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