Entropy-area law and temperature of de Sitter horizons from modular theory

Abstract

We derive an entropy-area law for the future horizon of an observer in diamonds inside the static patch of de Sitter spacetime, taking into account the backreaction of quantum matter fields. We prove positivity and convexity of the relative entropy for coherent states using Tomita--Takesaki modular theory, from which the QNEC for diamonds follows. Furthermore, we show that the generalized entropy conjecture holds. Finally, we reveal that the local temperature which is measured by an observer at rest exhibits subleading quantum corrections with respect to the well-known cosmological horizon temperature $H/(2\pi )$.

11 pages, 3 figures. Accepted for publication in PTEP

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Cited by in corpus (7)

• Modular Hamiltonian for de Sitter diamonds
• From Quantum Relative Entropy to the Semiclassical Einstein Equations
• Quantum information and the C-theorem in de Sitter
• Modular Hamiltonian for fermions of small mass
• Notions of Fermionic Entropies of a Causal Fermion System
• A numerical analysis of Araki-Uhlmann relative entropy in Quantum Field Theory
• Petz-Rényi relative entropy in QFT from modular theory