Global fluctuation spectra in big-crunch–big-bang string vacua

Abstract

We study big-crunch--big-bang cosmologies that correspond to exact world-sheet superconformal field theories of type II strings. The string theory spacetime contains a big crunch and a big bang cosmology, as well as additional ``whisker'' asymptotic and intermediate regions. Within the context of free string theory, we compute, unambiguously, the scalar fluctuation spectrum in all regions of spacetime. Generically, the big crunch fluctuation spectrum is altered while passing through the bounce singularity. The change in the spectrum is characterized by a function $\ensuremath{\Delta},$ which is momentum and time dependent. We compute $\ensuremath{\Delta}$ explicitly and demonstrate that it arises from the whisker regions. The whiskers are also shown to lead to ``entanglement'' entropy in the big bang region. Finally, in the Milne orbifold limit of our superconformal vacua, we show that $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}1$ and, hence, the fluctuation spectrum is unaltered by the big-crunch--big-bang singularity. We comment on, but do not attempt to resolve, subtleties related to gravitational back reaction and light winding modes when interactions are taken into account.