Geometries with mismatched branes

Abstract

We study Randall-Sundrum two brane setups with mismatched brane tensions. For the vacuum solutions, boundary conditions demand that the induced metric on each of the branes is either de Sitter, Anti-de Sitter, or Minkowski. For incompatible boundary conditions, the bulk metric is necessarily time-dependent. This introduces a new class of time-dependent solutions with the potential to address cosmological issues and provide alternatives to conventional inflationary (or contracting) scenarios. We take a first step in this paper toward such solutions. One important finding is that the resulting solutions can be very succinctly described in terms of an effective action involving only the induced metric on either one of the branes and the radion field. But the full geometry cannot necessarily be simply described with a single coordinate patch. We concentrate here on the time- dependent solutions but argue that supplemented with a brane stabilization mechanism one can potentially construct interesting cosmological models this way. This is true both with and without a brane stabilization mechanism.

Bubble needs strings

“…We will further see that this is precisely the dynamics in the bulk that saves us from the undesirable time dependence, which was a concern in some recent papers [11,12]. In the context of a 2-brane model, [12] showed that the effective G 4 depends on the time dependent relative position (parametrized by the radion) of a cutoff brane. They did find that a change of frame to Einstein frame actually makes G 4 time independent, but this was of no help since any matter dependent on the radion would have the undesired time dependence.…”

“…We perform a JHEP03(2021)250 worldsheet analysis to understand their role in producing four dimensional gravity on the shellworld, and comment on the analogy between mass renormalization and holographic renormalization. In section 4, we comment on the time dependence that was pointed out in recent results of [11,12] and how it is evaded in the shellworld construction. Finally, we conclude with a summary in section 5.…”

“…Alternatively, one can trade off the spacetime dependence of G 4 at the price of introducing a five dimensional spacetime dependent bulk scalar field, the radion field, which can be interpreted as the distance between the two branes. This point of view was adopted in a recent work [12].…”

“…In this section, we will comment on some recent work [11,12] and its connection to our model of a dark bubble. In particular, we will address the issue of residual time-dependence.…”

“…In particular, we will address the issue of residual time-dependence. In [12], the authors considered a generalized two brane model with "mismatching" tension in order to have a time evolving de Sitter braneworld. They showed that one can obtain de Sitter in the Einstein frame with a time independent G 4 .…”