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The general formalism of the free Dirac fermions on spatially flat$(1+3)$-dimensional Friedmann-Lema\^ itre-Robertson-Walker (FLRW) spacetimes isdeveloped in momentum representation. The mode expansions in terms of thefundamental spinors satisfying the charge conjugation and normalizationconditions are used for deriving the structure of the anti-commutatormatrix-functions and, implicitly, of the retarded, advanced, and Feynmanfermion propagators. The principal result is that the new type of integralrepresentation we proposed recently in the de Sitter case can be applied to theDirac fermions in any spatially flat FLRW geometry. Moreover, the Diracequation of the left-handed massless fermions can be analytically solvedfinding a general spinor solution and deriving the integral representations ofthe neutrino propagators. It is shown that in the Minkowski flat spacetime ournew integral representation is up to a change of variable just like the usualFourier representation of the fermion propagators. The form of the Feynmanpropagator of the massive fermions on a spatially flat FLRW spacetime with ascale factor of Milne-type is also outlined.

Propagators of the Dirac fermions on spatially flat FLRW spacetimes