The bimetric variational principle for General Relativity

TL;DR

This paper introduces a bimetric variational principle for general relativity, leading to a theory with propagating torsion and new degrees of freedom, distinct from traditional formalisms, with potential for ghost-free models.

Contribution

It proposes a novel bimetric variational approach that generates a physically distinct theory with propagating torsion and explores conditions for ghost-free models.

Findings

Propagating torsion naturally arises from the new variational principle.

Certain simple actions yield viable linearized theories without ghosts.

Nonlinear interactions may introduce ghost-like degrees of freedom, requiring further investigation.

Abstract

The bimetric variational principle is a subtle reinterpretation of general relativity that assumes the spacetime connection to be generated by an independent metric. Unlike the so called Palatini formalism that promotes the connection into a fundamental field, the new variational principle results in a physically distinct theory since the potential for the connection carries new degrees of freedom. The connection-generating metric naturally allows also an antisymmetric component. This sets torsion propagating! It is also shown here that while in the most straightforward generalization of the Einstein-Hilbert action the nonmetric degrees of freedom become ghosts, there exist very simple actions which give rise to viable theories at the linearised level when subjected to the bimetric variational principle. However, the non linear interactions might bring unpleasant features like the Boulware-Deser ghost. This remains to be explored since this new type of bimetric theories does not, in principle, lie in the class of usual bimetric theories where non-linear interactions inevitably come in with new ghost-like degrees of freedom.