Bent Domain Walls as Braneworlds

TL;DR

Kaloper analyzes bent domain walls in a 5D curved background as a tractable braneworld model. He constructs a wide class of exact one- and two-wall solutions with locally constant bulk and wall curvature, showing wall curvature can be much smaller than tension, allowing partial cancellation of the bulk cosmological constant on each wall while leaving a residual cosmological constant still larger than observational bounds, and derives the single-wall relation $H^2 = \frac{\kappa_5^2}{36}(\kappa_5^2 \sigma^2 - 6\Lambda)$ with warp factor $a(w)$ given by a hyperbolic combination. In the two-wall case, parallel branes admit matching conditions that fix their separation and warp factors (and can produce horizons in the bulk), yielding AdS4 or FRW-like slices on the branes depending on parameters. The work highlights a hybrid of Savas and RS ideas, shows partial CC screening is possible geometrically, and discusses implications for brane inflation, albeit noting the simplest setups do not reach the observed tiny cosmological constant without further ingredients.

Abstract

We consider domain walls embedded in curved backgrounds as an approximation for braneworld scenarios. We give a large class of new exact solutions, exhausting the possibilities for describing one and two walls for the cases where the curvature of both the bulk and the wall is locally constant. In the case of two walls, we find solutions where each wall has positive tension. An interesting property of these solutions is that the curvature of the walls can be much smaller than the tension, leading to a significant cancellation of the effective cosmological constant, which however is still much larger than the observational limits. We further discuss some aspects of inflation in models based on wall solutions.