Einstein static universe as a brane in extra dimensions

TL;DR

This paper proposes a brane-world model where the universe resembles Einstein's static universe with extra dimensions, leading to unique geometric properties and effective 4D gravity at intermediate scales.

Contribution

It introduces a novel brane-world scenario with a compact S^4 topology that reproduces Einstein's static universe and exhibits distinctive geometric and gravitational features.

Findings

Effective 4D gravity at intermediate scales with large distance corrections.

The universe's topology allows for geodesic completeness unlike in Randall-Sundrum models.

Physical distances between points on the brane are of the order of the extra dimension size.

Abstract

We present a brane-world scenario in which two regions of $AdS_5$ space-time are glued together along a 3-brane with constant positive curvature such that {\em all} spatial dimensions form a compact manifold of topology $S^4$. It turns out that the induced geometry on the brane is given by Einstein's static universe. It is possible to achieve an anisotropy of the manifold which allows for a huge hierarchy between the size of the extra dimension $R$ and the size of the observable universe $R_U$ at present. This anisotropy is also at the origin of a very peculiar property of our model: the physical distance between {\em any two points} on the brane is of the order of the size of the extra dimension $R$ regardless of their distance measured with the use of the induced metric on the brane. In an intermediate distance regime $R \ll r \ll R_U$ gravity on the brane is shown to be effectively 4-dimensional, with corresponding large distance corrections, in complete analogy with the Randall-Sundrum II model. For very large distances $r \sim R_U$ we recover gravity in Einstein's static universe. However, in contrast to the Randall-Sundrum II model the difference in topology has the advantage of giving rise to a geodesically complete space.