T-Duality and Time development of a (2+1)-Dimensional String Universe

TL;DR

This paper investigates the time evolution of a (2+1)-dimensional string universe, revealing how the geometry and cycle lengths evolve over time depending on the rationality of a key parameter.

Contribution

It provides a detailed analysis of the dynamics of a (2+1)-dimensional string universe using background field equations derived from string theory, highlighting the role of a real parameter in the universe's evolution.

Findings

For rational parameters, the universe stretches along one cycle while the other remains finite.

For irrational parameters, cycle lengths and volume grow proportionally with proper time.

The model characterizes different asymptotic behaviors based on the rationality of the parameter.

Abstract

The time development of a model of (2+1)-dimensional torus universe is studied based on background field equations which follow from a string theory. The metrics in various cases are characterized by a real parameter which specifies a ratio of the lengths of two independent cycles. When the parameter is a rational number, the space is asymptotically stretched along a cycle while the other cycle kept finite. When the parameter is an irrational number, the lengths of two cycles, as well as the space volume (area), grow in proportion to the proper time $t$ for an observer sitting at rest in this universe in the asymptotic region.