Supercriticality of a Class of Critical String Cosmological Solutions

TL;DR

This paper investigates a class of string cosmological solutions with hyperbolic spatial slices, revealing they are supercritical due to modular invariance, and discusses implications for why our universe is four-dimensional.

Contribution

It demonstrates that certain critical dimension string cosmological solutions are actually supercritical, providing insights into the dimensionality of our universe and connections to Supercritical String Cosmology.

Findings

The solutions are supercritical due to modular invariance.

All simple nontrivial string cosmological solutions are supercritical.

Provides a possible explanation for our universe being four-dimensional.

Abstract

For a class of Friedmann-Robertson-Walker type string solutions with compact hyperbolic spatial slices formulated in critical dimension, we find the world sheet conformal field theory which involves the linear dilaton and Wess-Zumino-Witten type model with the compact hyperbolic target space. By analyzing the infrared spectrum, we conclude that the theory is actually supercritical due to the modular invariance of string theory. Thus, taking into account previous results, we conclude that all the simple nontrivial string cosmological solutions are supercritical. A possible explanation of why we are living in D=4 is provided. The interesting relation of this background with the Supercritical String Cosmology (SSC) is pointed out.