Fermions on spacetimes of spatially closed hypersurfaces

Using a convenient compact time-like coordinate f ∈ [0, 1], characterizing the whole big bang–big crunch spacetime history cyclicly evolving with a 2π conformal period, we write down the Dirac-type equation in a FRW matter-dominated Universe. It turns out that, by accepting the idea of existence of an alternative time gauge, as for example in the projected Universe, one is able to derive closed form solutions, for physically meaningful cases.