Bulk spacetimes for cosmological braneworlds with a time-dependent extra dimension

Abstract

We explore the possibilities of constructing bulk spacetimes in five dimensions for warped braneworld models with a spatially flat Friedmann-Robertson-Walker (FRW) line element on the 3-brane and with a time-dependent extra dimension. Our first step in this direction involves looking at the status of energy conditions when such a bulk line element is assumed. We check these conditions by analysing the relevant inequalities, for specific functional forms (chosen to satisfy certain desirable features) of the warp factor, the cosmological scale factor and the extra-dimensional scale factor. Subsequently, we aim at obtaining solutions with different types of bulk matter sources.We begin with a general analysis of the solution space of non-singular Randall-Sundrum type bulk models with an exponential warp factor and a chosen equation of state. Thereafter, we focus on three specific bulk sources -the ordinary scalar field, the Brans-Dicke scalar and the dilaton. In each case, we are able to solve the field equations and obtain desirable solutions for which, we once again check the viability of the energy conditions. We also show how one can place branes in the bulk using the junction conditions. The issue of resolution of the bulk singularities which appear in our solutions, using standard methods, is also presented briefly. In summary, we are able to demonstrate, that it is indeed possible to construct viable bulk spacetimes for warped cosmological braneworlds with a time-varying extra dimension and with bulk matter satisfying the energy conditions.

Spin1/2field and regularization in a de Sitter and radiation dominated universe

“…In future, we plan to apply this formalism in other cosmological scenarios of interest e.g. during an anisotropic collapse [17] or in a warped cosmological braneworld [47].…”

Generalised Ellis–Bronnikov wormholes embedded in warped braneworld background and energy conditions

“…The domain of y, which is the extra spatial dimension, can be −∞ < y < ∞. In the following, we shall set f (y) = ± log[cosh(y/y 0 )], which correspond to the well-known thick brane models [94,95]. In such models, the brane is dynamically generated as a scalar field domain wall in the bulk.…”

“…The family of wormholes we choose for embedding is based on [91] where the well-known Ellis-Bronnikov (EB) spacetime [92,93] had been extended to provide a generalised family (GEB) of spacetimes that satisfies the null energy condition and further detailed studies is done in [69]. For bulk geometry, we choose the so-called thick braneworld scenario [94,95] where the growing or decaying warping factor is a smooth function of the extra dimension and thus represent thick domain wall solutions. A thick brane scenario is preferred over the originally proposed infinitely thin Randall-Sundrum-branes as the former do not introduce Dirac delta functions in the field equations and they naturally appear if one takes into account quantum effects and minimum length scales.…”

Generalised Ellis-Bronnikov wormholes embedded in warped braneworld background and energy conditions

“…The family of wormholes we choose for embedding is based on [91] where the well-known Ellis-Bronnikov (EB) spacetime [92,93] had been extended to provide a generalised family (GEB) of spacetimes that satisfies the null energy condition and further detailed studies is done in [69]. For bulk geometry, we choose the so-called thick braneworld scenario [94,95] where the growing or decaying warping factor is a smooth function of the extra dimension and thus represent thick domain wall solutions. A thick brane scenario is preferred over the originally proposed infinitely thin Randall-Sundrumbranes as the former do not introduce Dirac delta functions in the field equations and they naturally appear if one takes into account quantum effects and minimum length scales.…”

“…which correspond to the well-known thick brane models [94,95]. In such models, the brane is dynamically generated as a scalar field domain wall in the bulk.…”