Homogeneity, Flatness and "Large" Extra Dimensions

TL;DR

This paper proposes a model with extra dimensions and a hyperbolic manifold that naturally explains the universe's homogeneity and flatness through entropy smoothing mechanisms, without requiring fine-tuning of fundamental parameters.

Contribution

It introduces a cosmological model with hyperbolic extra dimensions that accounts for homogeneity and flatness via entropy smoothing, avoiding fine-tuning of physical scales.

Findings

Entropy smoothing explains universe homogeneity.

Model allows fundamental scale ≥ 1 TeV.

Large dimensionless numbers arise from topology.

Abstract

We consider a model in which the universe is the direct product of a (3+1)-dimensional Friedmann, Robertson-Walker (FRW) space and a compact hyperbolic manifold (CHM). Standard Model fields are confined to a point in the CHM (i.e. to a brane). In such a space, the decay of massive Kaluza-Klein modes leads to the injection of any initial bulk entropy into the observable (FRW) universe. Both Kolmogoro-Sinai mixing due to the non-integrability of flows on CHMs and the large statistical averaging inherent in the collapse of the initial entropy onto the brane smooth out any initial inhomogeneities in the distribution of matter and of 3-curvature on any slice of constant 3-position. If, as we assume, the initial densities and curvatures in each fundamental correlation volume are drawn from some universal underlying distributions independent of location within the space, then these smoothing mechanisms effectively reduce the density and curvature inhomogeneities projected onto the FRW. This smoothing is sufficient to account for the current homogeneity and flatness of the universe. The fundamental scale of physics can be $\gsim 1$TeV. All relevant mass and length scales can have natural values in fundamental units. All large dimensionless numbers, such as the entropy of the universe, are understood as consequences of the topology of spacetime which is not explained. No model for the origin of structure is proffered.