Inflating wormholes in the braneworld models

The braneworld model, in which our Universe is a three-brane embedded in a five-dimensional bulk, allows the existence of wormholes, without any violation of the energy conditions. A fundamental ingredient of traversable wormholes is the violation of the null energy condition (NEC). However, in the braneworld models, the stress–energy tensor confined on the brane, threading the wormhole, satisfies the NEC. In conventional general relativity, wormholes existing before inflation can be significantly enlarged by the expanding spacetime. We investigate the evolution of an inflating wormhole in the braneworld scenario, in which the wormhole is supported by the nonlocal braneworld effects. As a first step in our study, we consider the possibility of embedding a four-dimensional braneworld wormhole into a five-dimensional bulk. The conditions for the embedding are obtained by studying the junction conditions for the wormhole geometry, as well as the full set of the five-dimensional bulk field equations. For the description of the inflation, we adopt the chaotic inflation model. We study the dynamics of the braneworld wormholes during the exponential inflation stage, and in the stage of the oscillating scalar field. A particular exact solution corresponding to a zero redshift wormhole is also obtained. The resulting evolution shows that while the physical and geometrical parameters of a zero redshift wormhole decay naturally, a wormhole satisfying some very general initial conditions could turn into a black hole and exist forever.