Cosmological expansion on a dilatonic brane-world

Abstract

In this paper we study brane-world scenarios with a bulk scalar field, using a covariant formalism to obtain a 4D Einstein equation via projection onto the brane. We discuss, in detail, the effects of the bulk on the brane and how the scalar field contribute to the gravitational effects. We also discuss choice of conformal frame and show that the frame selected by the induced metric provides a natural choice. We demonstrate our formalism by applying it to cosmological scenarios of Randall-Sundrum and Hořava-Witten type models. Finally we consider the cosmology of models where the scalar field couples non-minimally to the matter on the brane. This gives rise to a novel scenario where the universe expands from a finite scale factor with an initial period of accelerated expansion, thus avoiding the singularity and flatness problem of the standard big bang model.

Hubble law and brane matter after ekpyrosis

“…Cosmology on the branes in the case of a scalar field with a potential in the bulk and on the branes has been studied in [26][27][28][29].…”

“…8 It is notable that in the ekpyrotic model, this term is exactly cancelled by a contribution from the bulk curvature, leaving a vanishing effective cosmological constant on the brane. See also [27].…”

Brane cosmology solutions with bulk scalar fields

“…One possibility is to to make assumptions about the bulk solution near the brane [4,5], although we will not know if they are justified or not. A preferable option is to solve the full higher dimensional Einstein equations.…”

Restrictions on Dilatonic Brane-World Models

“…There is an extensive list of papers devoted to the investigation of the dilatonic brane-world models with a slightly different form of the action (e.g. [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]). They naturally follows from a low-energy limit of string theories and have a dilatonic bulk potential and a dilatonic coupling potential of the form of 1 We should emphasize that in the standard Kaluza-Klein model the interaction (with c 0 ∼ 1/M Pl ) between graviscalars (gravexcitons [5]) and massless particles is possible at tree level [6].…”

“…It would be very interesting to find explicit models leading to such stabilization. If, in general, such stabilization is 5 An effective energy-momentum conservation equation for the matter on the brane has the form [17] (f (ϕ)T…”