Entanglement production in Einstein-Cartan theory

TL;DR

This paper investigates how torsion in Einstein-Cartan theory influences entanglement production in Dirac and Klein-Gordon fields within an expanding universe, revealing torsion's role in enhancing or modifying entanglement entropy.

Contribution

It provides the first detailed analysis of torsion effects on quantum entanglement in cosmological models for both Dirac and Klein-Gordon fields, including exact solutions and physical interpretations.

Findings

Torsion increases entanglement for Dirac fields, especially at low momenta.

Exact solutions show how torsion modifies entanglement in Klein-Gordon fields.

Comparison with torsion-free models highlights the impact of torsion on quantum correlations.

Abstract

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.