  Time reversal invariant (TRI) topological superfluids (TSFs) and topological
superconductors (TSCs) are robust symmetry protected gapped topological states.
In this article, we study the evolution of these topological states in the
presence of time reversal symmetry breaking (TRB) fields and/or sufficiently
large TRI fields. Physically, one of the realizations of TRB fields can be
internal spin exchange fields due to background magnetic ordering. We find that
the fully gapped TSFs and TSCs are generically separated from other nodal
states by various zero temperature quantum critical points that are
characterized by generalized quantum Lifshitz fields with distinct scaling
properties. These emergent Lifshitz fields also define finite temperature
properties in quantum critical regimes. Moreover, for a certain subset of TRB
fields, there exist a precursor to bulk transitions, where surface states can
also exhibit quantum critical behavior near zero fields. The possibility for a
fully gapped TSF/TSC to smoothly crossover into a topologically trivial state
without a phase transition is also examined.
