Can gravitational dynamics be obtained by diffeomorphism invariance of action?

TL;DR

The paper argues that gravitational dynamics are inherently diffeomorphism invariant due to the nature of the action, challenging recent proposals that derive gravity solely from this invariance.

Contribution

It clarifies that the standard construction of the gravitational action is already diffeomorphism invariant, invalidating the alternative approach that derives gravity from this invariance alone.

Findings

Standard gravitational action is inherently diffeomorphism invariant.

The alternative derivation of gravity from invariance is flawed.

Technical errors exist in the proposed alternative approach.

Abstract

It has recently been suggested that the gravitational dynamics could be obtained by requiring the action to be invariant under diffeomorphism transformations. We argue that the action constructed in usual way is automatically diffeomorphism invariant in nature, which thus invalidates this alternative perspective to obtain gravitational dynamics. Especially, we also show what is wrong with the technical derivation of gravitational dynamics in the alternative approach.