Global Fluctuation Spectra in Big Crunch/Big Bang String Vacua
Ben Craps, Burt A. Ovrut
TL;DR
The paper investigates how scalar fluctuations propagate through Big Crunch/Big Bang transitions in string theory by analyzing exact generalized Milne orbifold vacua with whisker regions. Using globally defined string-theoretic wavefunctions, it computes the full fluctuation spectrum across all regions and expresses the post-bounce spectrum change via a momentum- and time-dependent factor $Δ(\vec{k},t)$, which is tied to whisker physics and potential information loss. In the Milne orbifold limit, $Δ\to1$, leaving the spectrum invariant through the bounce, while in generalized Milne orbifolds the whiskers induce nontrivial spectral modifications and entanglement entropy between late-time Big Bang and whisker regions. The work highlights how stringy geometry, backreaction considerations, and winding modes shape pre- to post-bounce cosmological perturbations and offers a controlled framework for connecting early-universe physics to string theory observables.
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 $Δ$, which is momentum and time-dependent. We compute $Δ$ 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 $Δ\to 1$ 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 backreaction and light winding modes when interactions are taken into account.