String spectra near some null cosmological singularities

TL;DR

This paper constructs null cosmological singularities as gravitational solutions, analyzes string spectra near these singularities, and finds that low-lying modes remain finite while high-oscillation modes propagate freely, indicating significant string interactions.

Contribution

It provides an exact solution for string modes near null Kasner-like singularities and studies their behavior, revealing finite low-lying modes and free high-oscillation modes.

Findings

Low-lying string modes are non-divergent near singularities.

High-oscillation string modes propagate freely, indicating weak coupling.

String interactions become significant close to the singularity.

Abstract

We construct cosmological spacetimes with null Kasner-like singularities as purely gravitational solutions with no other background fields turned on. These can be recast as anisotropic plane-wave spacetimes by coordinate transformations. We analyse string quantization to find the spectrum of string modes in these backgrounds. The classical string modes can be solved for exactly in these time-dependent backgrounds, which enables a detailed study of the near singularity string spectrum, (time-dependent) oscillator masses and wavefunctions. We find that for low lying string modes(finite oscillation number), the classical near-singularity string mode functions are non-divergent for various families of singularities. Furthermore, for any infinitesimal regularization of the vicinity of the singularity, we find a tower of string modes of ultra-high oscillation number which propagate essentially freely in the background. The resulting picture suggests that string interactions are non-negligible near the singularity.