Bouncing branes

We investigate (4 + 1)- and (5 + 0)-dimensional gravity coupled to a non-compact scalar field sigma-model in the context of a single-brane-world scenario with separable metric and a bulk fluid. We briefly discuss the standard cosmological solutions and the family of warp factors (which includes both the original Randall-Sundrum [Phys. Rev. Lett. 83 (1999) 3370, hep-ph/9905221; Phys. Rev. Lett. 83 (1999) 4690, hep-th/9906064] solution and the solution of Kachru, Schulz and Silverstein [H.A. Chamblin, H.S. Reall, Nucl. Phys. B 562 (1999) 133, hep-th/9903225; S. Kachru, M. Schulz, E. Silverstein, Phys. Rev. D 62 (2000) 045021, hep-th/0001206]) for the case of a rolling fifth radius [C. Kennedy, E.M. Prodanov, Phys. Lett. B 488 (2000) 11, hep-th/0003299]. We show how this model can be adjusted so that it describes the standard cosmology on a self-tuning domain wall (with static fifth radius) [C. Kennedy, E.M. Prodanov, hep-th/0010202] and we discuss the solutions. Searching for a possible relation to the negative Euclidean stress energy, appearing in the Giddings and Strominger's axion induced topology change in quantum gravity and string theory [S.B. Giddings, A. Strominger, Nucl. Phys. B 306 (1988) 890], we modify the non-compact sigma-model into a single-field model (with a rolling fifth radius, separable metric, and no bulk fluid) for the more general case of a brane with non-zero curvature parameter. We find a solution (with a Kachru-Schulz-Silverstein warp factor [Phys. Rev. D 62 (2000) 045021, hep-th/0001206]), representing a Tolman wormhole for a R × S³ brane with Lorentz metric and for a R × AdS₃ brane with positive definite metric.