On the properties of the irrotational dust model

TL;DR

This paper clarifies that the irrotational dust model's Hamiltonian not being a square root is solely due to the time-gauge choice, resolving a recent debate in the literature.

Contribution

It demonstrates that the non-square root form of the Hamiltonian arises directly from the time-gauge choice without extra assumptions.

Findings

Hamiltonian is not a square root due to time-gauge choice

Clarifies a debated point in the literature

No additional assumptions needed for this property

Abstract

In this note we analyze the model of the irrotational dust used recently to deparametrize gravitational action. We prove that the remarkable fact that the Hamiltonian is not a square root is a direct consequence of the time-gauge choice in this model. No additional assumptions or sign choices are necessary to obtain this crucial feature. In this way we clarify a point recently debated in the literature.