  We study the entanglement production for Dirac and Klein-Gordon fields in an
expanding spacetime characterized by the presence of torsion. Torsion is here
considered according to the Einstein-Cartan theory with a conformally flat
Friedmann-Robertson-Walker spacetime. In this framework, torsion is seen as an
external field, fulfilling precise constraints directly got from the
cosmological constant principle. For Dirac field, we find that torsion
increases the amount of entanglement. This turns out to be particularly evident
for small values of particle momentum. We discuss the roles of Pauli exclusion
principle in view of our results, and, in particular, we propose an
interpretation of the two maxima that occur for the entanglement entropy in
presence of torsion. For Klein-Gordon field, and differently from the Dirac
case, the model can be exactly solved by adopting the same scale factor as in
the Dirac case. Again, we show how torsion affects the amount of entanglement,
providing a robust physical motivation behind the increase or decrease of
entanglement entropy. A direct comparison of our findings is also discussed in
view of previous results derived in absence of torsion. To this end, we give
prominence on how our expectations would change in terms of the coupling
between torsion and the scale factor for both Dirac and Klein-Gordon fields.
