ADM Analysis of Gravity Models within the Framework of Bimetric Variational Formalism

TL;DR

This paper applies ADM decomposition to bimetric variational formalism in gravity models, demonstrating instability in linear models, difficulty in constructing ghost-free non-linear models, and proposing a viable scalar field model.

Contribution

It introduces the ADM analysis to bimetric variational gravity models, revealing stability issues and proposing a new viable scalar field model within this framework.

Findings

Linear models are unstable as shown by ADM analysis.

Constructing ghost-free non-linear models is highly challenging.

A viable scalar field gravity model is constructed as a proof of principle.

Abstract

Bimetric variational formalism was recently employed to construct novel bimetric gravity models. In these models an affine connection is generated by an additional tensor field which is independent of the physical metric. In this work we demonstrate how the ADM decomposition can be applied to study such models and provide some technical intermediate details. Using ADM decomposition we are able to prove that a linear model is unstable as has previously been indicated by perturbative analysis. Moreover, we show that it is also very difficult if not impossible to construct a non-linear model which is ghost-free within the framework of bimetric variational formalism. However, we demonstrate that viable models are possible along similar lines of thought. To this end, we consider a set up in which the affine connection is a variation of the Levi-Civita one. As a proof of principle we construct a gravity model with a massless scalar field obtained this way.