String--Kaluza--Klein Cosmology

TL;DR

The paper develops isotropic cosmologies by twisting a five-dimensional string-theory black-hole solution and performing Kaluza--Klein reduction to four dimensions, obtaining a FRW-like metric accompanied by a dilaton, a modulus, and torsion for arbitrary spatial curvature $k$. It derives the corresponding four-dimensional effective action and analyzes the cosmological dynamics in both string and Einstein frames, highlighting a duality that inverts the modulus and an exact conformal-field-theory limit in the extremal case $t_+^2 = k t_-^2$. Depending on $k$, the model exhibits oscillating universes ($k=1$) and wormhole-like geometries ($k=0,-1$), with frame-dependent singularities that are complementary between frames. The work also discusses the role of winding modes in traversing wormholes and the conditions under which dust can be consistently included, linking exact CFT constructions to string-inspired cosmology. These results provide a bridge between higher-dimensional string theory and 4D cosmological scenarios, suggesting directions for exact higher-dimensional solutions using gauged WZW models.

Abstract

We generalize a five dimensional black hole solution of low energy effective string theory to arbitrary constant spatial curvature. After interchanging the signature of time and radius we reduce the 5d solution to four dimensions and obtain that way a four dimensional isotropic cosmological space time. The solution contains a dilaton, modulus field and torsion. Several features of the solution are discussed.

Figures (2)

• Figure 1:
• Figure 2: In (a) we have plotted the closed oscillating solution for $k=1$ and (b) is the wormhole solution for $k=-1$. Below are the both extremal limits: (c) corresponding to $R \times S_k^3$ and (d) the throat solution with one flat region for $k=-1$.