  The Kibble-Zurek mechanism (KZM) predicts that the average number of
topological defects generated upon crossing a continuous or quantum phase
transition obeys a universal scaling law with the quench time. Fluctuations in
the defect number near equilibrium are approximately of Gaussian form, in
agreement with the central limit theorem. Using large deviations theory, we
characterize the universality of fluctuations beyond the KZM and report the
exact form of the rate function in the transverse-field quantum Ising model. In
addition, we characterize the scaling of large deviations in an arbitrary
continuous phase transition, building on recent evidence establishing the
universality of the defect number distribution.
