Free energy and entropy in Rindler and de Sitter space-times

Abstract

We investigate the free energy and entropy of the Gaussian massive scalar field theory in the static de Sitter space-time for arbitrary temperature. For the inverse temperatures of the form $\beta =2\pi 2^k,k\in \mathbf{Z}$, in curvature units, we find the explicit form of the free energy and its derivatives with respect to the temperature. There are two types of contributions to the free energy: one is of the "area type" and can be attributed to the horizon, while the other is of the "volume type" and is associated with the interior of the space-time. The latter contribution in the odd-dimensional case in the limit of the week field (large mass or small Hubble constant) significantly depends on the temperature. Namely, for $\beta <2\pi$, the free energy behaves as $F_{\beta }^{bulk}\sim e^{-\beta m}$, while for $\beta >2\pi$ it behaves as $F_{\beta }^{bulk}\sim e^{-2\pi m}$. We also show that even the leading UV contributions to the free energy significantly depend on the state of the theory, which is very unusual. We explain the origin and physical meaning of these observations. As the model example we consider the situation in the Rindler wedge of the flat space-time.

27 pages

References in corpus (7)

• Universal terms for the entanglement entropy in 2+1 dimensions
• Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
• Heating up an environment around black holes and inside de Sitter space
• Large-order Perturbation Theory and de Sitter/Anti de Sitter Effective Actions
• Curved space equilibration vs. flat space thermalization (a short review)
• Characters, quasinormal modes, and Schwinger pairs in $d{S}_2$ with flux
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Cited by in corpus (8)

• On the global temperature of the Schwarzschild-de Sitter spacetime
• Isometry invariance of exact correlation functions in various charts of Minkowski and de Sitter spaces
• TCC bounds on the static patch of de Sitter space
• On Aspects of Spontaneous Symmetry Breaking in Rindler and Anti-de Sitter spacetimes for the $O(N)$ Linear Sigma Model
• Is the Euclidean path integral always equal to the thermal partition function?
• On the backreaction issue for the black hole in de Sitter space-time
• De Sitter entropy: on-shell versus off-shell
• On the Observer Dependence of the Quantum Effective Potential