Null cosmological singularities and free strings: II

TL;DR

This paper investigates null cosmological singularities and free string behavior, showing that certain singularities admit nonsingular wavefunctionals and analyzing observable differences in various variable descriptions.

Contribution

It identifies conditions under which null singularities allow nonsingular string wavefunctionals and compares physical observables across different variable frameworks.

Findings

Certain singularities admit a Rosen-Kasner frame with nonsingular wavefunctional time dependence

Observables without time derivatives are identical across variable choices

Some free string observables remain divergent near singularities

Abstract

In arXiv:0909.4731 [hep-th], we argued that the free string lightcone Schrodinger wavefunctional in the vicinity of null Kasner-like cosmological singularities has nonsingular time-dependence if the Kasner exponents satisfy certain relations. These backgrounds are anisotropic plane waves with singularities. We first show here that only certain singularities admit a Rosen-Kasner frame with exponents satisfying relations leading to a wavefunctional with nonsingular time-dependence. Then we build on the (Rosen) description further and study various physical observables for a time-dependent harmonic oscillator toy model and then the free string, reconciling this with the corresponding description in the conventional plane wave variables. We find that observables containing no time derivatives are identical in these variables while those with time derivatives are different. Various free string observables are still divergent, perhaps consistent with string oscillator states becoming light in the vicinity of the singularity.