Aether scalar tensor theory: Hamiltonian Formalism

TL;DR

This paper develops a Hamiltonian formalism for the Aether Scalar Tensor theory, clarifying its degrees of freedom and constraints, which is essential for understanding perturbations and stability in modified gravity models.

Contribution

It provides the first non-perturbative Hamiltonian formulation of the AeST theory, identifying its constraints and physical degrees of freedom.

Findings

Identified four first class and four second class constraints.

Determined the theory has six physical degrees of freedom.

Analyzed perturbations around Minkowski spacetime.

Abstract

The Aether Scalar Tensor (AeST) theory is an extension of General Relativity (GR), proposed for addressing galactic and cosmological observations without dark matter. By casting the AeST theory into a $3+1$ form, we determine its full non-perturbative Hamiltonian formulation and analyse the resulting constraints. We find the presence of four first class and four second class constraints and show that the theory has six physical degrees of freedom at the fully nonlinear level. Our results set the basis for determining the propagation of perturbations on general backgrounds and we present the case of small perturbations around Minkowski spacetime as an example stemming from our analysis.