  We explore the connection between pair production of dark matter particles at
collider experiments and annihilation of dark matter in the early and late
universe, with a focus on the correlation between the two time-reversed
processes. We consider both a model-independent effective theory framework,
where the initial and final states are assumed to not change under
time-reversal, and concrete UV-complete models within the framework of
supersymmetric extensions to the Standard Model. Even within the effective
theory framework (where crossing symmetry is in some sense assumed), we find
that the predictions of that symmetry can vary by orders of magnitude depending
on the details of the selected effective interaction. Within the supersymmetric
models we consider, we find that there is an even wilder variation in the
expectations one can derive for collider observables based on cross-symmetric
processes such as having a thermal relic or given indirect dark matter
detection rates. We also explore additional "pitfalls" where na\"ive crossing
symmetry badly fails, including models with very light mediators leading to
Sommerfeld enhancements and/or dark matter bound states.
