Entanglement entropy of $N=2^{⁎}$ de Sitter vacuum

de Sitter vacuum of nonconformal gauge theories is non-equilibrium, manifested by a nonvanishing rate of the comoving entropy production at asymptotically late times. This entropy production rate is related to the entanglement entropy of the de Sitter vacuum of the theory. We use holographic correspondence to compute vacuum entanglement entropy density $s_{ent}$ of mass deformed $N=4$ supersymmetric Yang-Mills theory — the $N=2^{⁎}$ gauge theory — for various values of the masses and the coupling constant to the background space-time curvature. For a particular choice of the curvature coupling, the Euclidean model can be solved exactly using the supersymmetric localization. We show that $N=2^{⁎}$ de Sitter entanglement entropy is not the thermodynamic entropy of the localization free energy at de Sitter temperature. Neither it is related to the thermal entropy of de Sitter vacuum of pair-produced particles.