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It is well-known that the number of particles produced in cosmology, commonlydefined in the literature from the Fock space of the instantaneous hamiltonianof the canonically normalized fields, is ambiguous. On the other hand, theenergy computed from the energy-momentum tensor should be physical. We comparethe corresponding Fock spaces and relate them through a Bogolyubovtransformation. We find that for particles of spin $0$, $1$ and $3/2$ the twoFock spaces are different, whereas they are the same for spin $1/2$ fermions.For spin $0$ and $1$, for particles of high momenta the two Fock spaces align,as intuitively expected. For the spin $3/2$, one finds two puzzles. The firstone is that the two corresponding Fock spaces do not match even in the limit ofhigh momenta. The second is that whereas we provide evidence for theequivalence theorem between longitudinal gravitinos and the goldstino in termsof an exact matching between the lagrangians and the instantaneous hamiltoniansfor the canonically normalized fields, the energy operator computed from theRarita--Schwinger action does not seem to be captured in a simple way by thegoldstino action. Our results suggest a re-analysis of non-thermal gravitinoproduction in cosmology.

On energy and particle production in cosmology: the particular case of the gravitino