Null cosmological singularities and free strings: II

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.