Class of probe brane universes

Abstract

I examine the idea that our world is a branelike object of negligible influence on the bulk spacetime. No particular action functional is specified. Instead, the probe brane dynamics is derived from the universally valid stress-energy conservation equations. As an example, I study the case of a three-sphere in the five-dimensional Minkowski spacetime. The resulting four-universe turns out to depend on the equation of state of the brane constituent matter but differs from that of general relativity. One observes that, for every general relativistic universe, there exists a brane universe of equal geometry but a slightly different equation of state. As for the stability of brane universes, I find that no equation of state leads to a stable solution. However, the situation changes if the bulk spacetime has a Euclidean signature. In this case, a class of stable cosmological solutions is obtained. The brane vibrations are guided by the covariant Klein-Gordon equation with an effective metric of the Minkowski signature. It is this effective metric that local observers actually detect. As a consequence, the detected Universe is of bouncing type, with an accelerating expanding phase.