Hamiltonian structure of bi-gravity, problem of ghost and bifurcation

Abstract

We analyze the Hamiltonian structure of a general theory of bi-gravity where the interaction term is a scalar function of the form $V({\mathcal{X}}^n)$ where $\mathcal{X}$ may be $\sqrt{g^{-1}f}$ or $g^{-1}f$. We give necessary conditions for the interaction term of such a theory to be ghost free. We give a precise constraint analysis of the bi-gravity theory of Hassan- Rosen and show that the additional constraint which omit the ghost is just one possibility at the bifurcation point.

arXiv comment19 pages, published version

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• Gauge generator for bi-gravity and multi-gravity models