Sailing through the big crunch-big bang transition
  In a recent series of papers, we have shown that theories with scalar fields
coupled to gravity (e.g., the standard model) can be lifted to a Weyl-invariant
equivalent theory in which it is possible to unambiguously trace the classical
cosmological evolution through the transition from big crunch to big bang. The
key was identifying a sufficient number of finite, Weyl-invariant conserved
quantities to uniquely match the fundamental cosmological degrees of freedom
across the transition. In so doing we had to account for the well-known fact
that many Weyl-invariant quantities diverge at the crunch and bang. Recently,
some authors rediscovered a few of these divergences and concluded based on
their existence alone that the theories cannot be geodesically complete. In
this note, we show that this conclusion is invalid. Using conserved quantities
we explicitly construct the complete set of geodesics and show that they pass
continuously through the big crunch-big bang transition.
