Dynamics of stringy congruence in early universe

TL;DR

This paper explores the behavior of stringy geodesic surface congruences in the early universe, deriving conditions for singularity formation and analyzing twist and shear effects within string theory cosmology.

Contribution

It extends the analysis of string congruences by deriving equations for twist and shear, and investigates singularity conditions using a Raychaudhuri-type equation in string theory.

Findings

Singularity conditions derived for stringy geodesic congruences.

Equations for twist and shear in terms of universe expansion.

Null string congruence behavior analyzed in appendix.

Abstract

We studied the singularity of the geodesic surface congruence for timelike and null strings using the expansion of the universe in the string theory. We had Raychaudhuri type equation for the expansion. Assuming the stringy strong energy condition and initial convergence, we induced the existence of singularity and got the same inequality equation of the string strong energy condition for both timelike and null stringy congruence. In this paper we want to study the twist and shear aspects of the stingy geodesic surface congruence. Under some natural conditions we derive the equations of the twist and the shear in terms of the expansion of the universe. In appendix we investigate the geodesic surface congruence of the null strings.