Abstract
We construct de Sitter branes in a flat bulk of massive gravity in 5D. We find two branches of solutions, reminiscent of the normal and self-accelerating branches in DGP, but with rather different properties. Neither branch has a self-accelerating limit: the background geometry requires having a nonvanishing tension. On the other hand, on both branches there are sub-branches where the leading order contributions of the tension to the curvature cancel. In these cases it turns out that larger tensions curve the background less. Further, both branches support a localized 4D massless graviton for a special choice of bulk mass terms. This choice may be protected by enhanced gauge symmetry. Finally, we generalize the solutions to the case of bigravity in a flat 5D bulk.
Highlights
Boundary terms in massive gravityWe begin by briefly reviewing the emergence of the brane terms required to covariantize the bulk masses in spacetimes with a boundary
In response it has been proposed that the theory can be improved by embedding massive gravity in warped extra dimensions
In the case of flat bulks this has been considered in an interesting article [23], which summarizes with a call for deployment of the “machinery” of [24] to study cosmology of such braneworlds and in particular their vacua, given by the geodesic worldvolumes of an empty, but possibly tensional brane in the bulk
Summary
We begin by briefly reviewing the emergence of the brane terms required to covariantize the bulk masses in spacetimes with a boundary. All that remains is to write down the explicit relationship of the embedding coordinates of 4D de Sitter in flat 5D bulk [25], which satisfy (2.4), and interpret the 5D coordinates of the embedding as the Stuckelberg fields This will yield the relationship between the intrinsic curvature length H, the tension σ and the bulk graviton mass m. What remains to determine is the relationship between the curvature radius 1/H, brane tension σ, and the scale which controls the IR modification of gravity, in this case the bulk graviton mass m. To this end we can turn to the equation (2.19), since the bulk equation (2.18) is trivially satisfied away from the brane cut. We will determine the ‘local’ Planck mass due to the zero mode and find that it is independent of the brane tension in the degravitating limit
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