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.
Highlights
In order to obtain the action of the low-energy effective theory written in terms of the metrics on the
(±)-branes, gμν, we solve the bulk equations for given boundary metrics gμν at the lowest order of the gradient expansion, and we integrate out the bulk degrees of freedom by substituting back the obtained bulk solution into the action and performing the integration along the extra dimension
We should interpret that the appearance of such extra degrees of freedom is responsible for the other bulk degrees of freedom with higher masses, which are in the present setup the massive KK gravitons with the mass squared of O(∆y −1 ) or higher
Summary
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