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 analyze 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 wave functions. We find that for low-lying string modes (finite oscillation number), the classical near-singularity string mode functions are nondivergent for various families of singularities. Furthermore, for any infinitesimal regularization of the vicinity of the singularity, we find a tower of string modes of ultrahigh oscillation number which propagate essentially freely in the background. The resulting picture suggests that string interactions are non-negligible near the singularity.

• Received 12 May 2009

DOI:https://doi.org/10.1103/PhysRevD.79.126009