Entanglement area law violation from field-curvature coupling

We investigate the ground state entanglement entropy of a massive scalar field nonminimally coupled to spacetime curvature, assuming a static, spherically symmetric background. We first discretize the field Hamiltonian by introducing a lattice of spherical shells and imposing a cutoff in the radial direction. We then study the ground state of the field and quantify deviations from area law due to nonminimal coupling, focusing in particular on Schwarzschild-de Sitter and Hayward spacetimes, also discussing de Sitter spacetime as a limiting case. We show that large positive coupling constants can significantly alter the entropy scaling with respect to the boundary area, in case of coordinate-dependent spacetime curvature. Our outcomes are interpreted in view of black hole entropy production and early universe scenarios.