Brane new world

Abstract

We study a Randall-Sundrum cosmological scenario consisting of a domain wall in anti-de Sitter space with a strongly coupled large N conformal field theory living on the wall. The AdS/CFT correspondence allows a fully quantum mechanical treatment of this CFT, in contrast with the usual treatment of matter fields in inflationary cosmology. The conformal anomaly of the CFT provides an effective tension which leads to a de Sitter geometry for the domain wall. This is the analogue of Starobinsky's four dimensional model of anomaly driven inflation. Studying this model in a Euclidean setting gives a natural choice of boundary conditions at the horizon. We calculate the graviton correlator using the Hartle-Hawking "No Boundary" proposal and analytically continue to Lorentzian signature. We find that the CFT strongly suppresses metric perturbations on all but the largest angular scales. This is true independently of how the de Sitter geometry arises, i.e., it is also true for four dimensional Einstein gravity. Since generic matter would be expected to behave like a CFT on small scales, our results suggest that tensor perturbations on small scales are far smaller than predicted by all previous calculations, which have neglected the effects of matter on tensor perturbations.

Braneworld models of dark energy

“…However, this term is qualitatively essential for describing the braneworld dynamics since it is inevitably generated as a quantum correction to the matter action in (1) -in the spirit of an idea that goes back to Sakharov [17] (see also [18]). Note that the effective action for the brane typically involves an infinite number of terms of higher order in curvature (this was pointed out in [14] for the case of braneworld theory; a similar situation in the context of the AdS/CFT correspondence is described in [19]). In this paper, we retain only the terms linear in curvature.…”

“…It should be pointed out that the static and empty braneworld solution described by (19) does not possess a general-relativistic analog, since, in general relativity, a static cosmological model (the 'static Einstein universe') cannot be empty (see, for instance, [4]). Furthermore, from (19) we find that the static empty universe…”

Randall–Sundrum brane tensions

“…Hints of this connection were made in [8,9,10,11], where the Randall-Sundrum II model was presented as an anti-de Sitter bulk theory with a boundary not at infinity but instead at some finite location. By pushing the boundary off to infinity, one finally decouples gravity and hence recovers the standard AdS/CFT relation.…”

Quantum (in)stability of a brane-world universe at nonzero temperature

“…There are various proposals for such a realization. For example, taking the quantum effects of brane CFT (via the corresponding conformal anomaly) may help in the construction of new brane-worlds [3][4][5][6] which occur in the AdS/CFT correspondence (as a kind of holographic renormalization group (RG) flow). It is remarkable that a calculation of corrections to Newton's law from quantum brane CFT coincides quite well with that computed from supergravity [7].…”