Bigravity from gradient expansion

TL;DR

This paper derives a ghost-free bigravity theory from a braneworld model using gradient expansion, revealing the graviton interactions and radion behavior without linear approximation.

Contribution

It demonstrates how ghost-free bigravity can emerge from a DGP two-brane setup via gradient expansion, including radion dynamics and nonlinear graviton interactions.

Findings

Effective bigravity is ghost free at leading order.

Graviton interactions follow Fierz-Pauli form.

Radion remains as a scalar with non-trivial coupling.

Abstract

We discuss how the ghost-free bigravity coupled with a single scalar field can be derived from a braneworld setup. We consider DGP two-brane model without radion stabilization. The bulk configuration is solved for given boundary metrics, and it is substituted back into the action to obtain the effective four-dimensional action. In order to obtain the ghost-free bigravity, we consider the gradient expansion in which the brane separation is supposed to be sufficiently small so that two boundary metrics are almost identical. The obtained effective theory is shown to be ghost free as expected, however, the interaction between two gravitons takes the Fierz-Pauli form at the leading order of the gradient expansion, even though we do not use the approximation of linear perturbation. We also find that the radion remains as a scalar field in the four-dimensional effective theory, but its coupling to the metrics is non-trivial.