  The violation of the Bell inequality for Dirac fermions is investigated in
the cosmological de Sitter spacetime, in the presence of background
electromagnetic fields of constant strengths. The orthonormal Dirac mode
functions are obtained and the relevant in-out squeezed state expansion in
terms of the Bogoliubov coefficients are found. We focus on two scenarios here
: strong electric field and heavy mass limits (with respect to the Hubble
constant). Using the squeezed state expansion, we then demonstrate the Bell
violations for the vacuum and some maximally entangled initial states. Even
though a background magnetic field alone cannot create particles, in the
presence of background electric field and or spacetime curvature, it can affect
the particle creation rate. Our chief aim thus here is to investigate the role
of the background magnetic field strength in the Bell violation. Qualitative
differences in this regard for different maximally entangled initial states are
shown. Further extension of these results to the so called $\alpha$-vacua are
also discussed.
