Abstract
Entanglement entropy (EE) of a spatial region quantifies correlations between the region and its surroundings. For a free scalar in the adiabatic vacuum in de Sitter space the EE is known to remain low, scaling as the surface area of the region. Here, we study the evolution of entanglement after the universe transitions from de Sitter to flat space. We concentrate on the case of a massless minimally coupled scalar. We find numerically that, after the de Sitter stage ends, the EE and the Ŕenyi entropy rapidly grow and saturate at values obeying the volume law. The final state of the subsystem (region) is a partially thermalized state reminiscent of a generalized Gibbs ensemble. We comment on application of our results to the question of when and how cosmological perturbations decohere.
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References
S. Khlebnikov and M. Kruczenski, Locality, entanglement, and thermalization of isolated quantum systems, Phys. Rev. E 90 (2014) 050101(R) [INSPIRE].
P. Calabrese and J.L. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. 0504 (2005) P04010 [cond-mat/0503393] [INSPIRE].
H. Casini, H. Liu and M. Mezei, Spread of entanglement and causality, JHEP 07 (2016) 077 [arXiv:1509.05044] [INSPIRE].
J.S. Cotler, M.P. Hertzberg, M. Mezei and M.T. Mueller, Entanglement growth after a global quench in free scalar field theory, JHEP 11 (2016) 166 [arXiv:1609.00872] [INSPIRE].
V.F. Mukhanov and G.V. Chibisov, Quantum fluctuations and a nonsingular universe, JETP Lett. 33 (1981) 532 [Pisma Zh. Eksp. Teor. Fiz. 33 (1981) 549] [INSPIRE].
S.W. Hawking, The development of irregularities in a single bubble inflationary universe, Phys. Lett. B 115 (1982) 295 [INSPIRE].
A.A. Starobinsky, Dynamics of phase transition in the new inflationary universe scenario and generation of perturbations, Phys. Lett. B 117 (1982) 175 [INSPIRE].
A.H. Guth and S.-Y. Pi, Fluctuations in the new inflationary universe, Phys. Rev. Lett. 49 (1982) 1110 [INSPIRE].
R. Brandenberger, V. Mukhanov and T. Prokopec, Entropy of the gravitational field, Phys. Rev. D 48 (1993) 2443 [gr-qc/9208009] [INSPIRE].
T. Prokopec, Entropy of the squeezed vacuum, Class. Quant. Grav. 10 (1993) 2295 [INSPIRE].
M. Gasperini and M. Giovannini, Entropy production in the cosmological amplification of the vacuum fluctuations, Phys. Lett. B 301 (1993) 334 [gr-qc/9301010] [INSPIRE].
M. Kruczenski, L.E. Oxman and M. Zaldarriaga, Large squeezing behavior of cosmological entropy generation, Class. Quant. Grav. 11 (1994) 2317 [gr-qc/9403024] [INSPIRE].
C. Kiefer, D. Polarski and A.A. Starobinsky, Entropy of gravitons produced in the early universe, Phys. Rev. D 62 (2000) 043518 [gr-qc/9910065] [INSPIRE].
J. Maldacena and G.L. Pimentel, Entanglement entropy in de Sitter space, JHEP 02 (2013) 038 [arXiv:1210.7244] [INSPIRE].
R. Simon, N. Mukunda and B. Dutta, Quantum-noise matrix for multimode systems: U(n) invariance, squeezing, and normal forms, Phys. Rev. A 49 (1994) 1567.
M. Rigol, V. Dunjko, V. Yurovsky and M. Olshanii, Relaxation in a completely integrable many-body quantum system: an ab initio study of the dynamics of the highly excited states of 1d lattice hard-core bosons, Phys. Rev. Lett. 98 (2007) 050405 [cond-mat/0604476].
P. Calabrese, F.H.L. Essler and M. Fagotti, Quantum quenches in the transverse field Ising chain: II. Stationary state properties, J. Stat. Mech. 2012 (2012) P07022 [arXiv:1205.2211].
M.P.A. Fisher, P.B. Weichman, G. Grinstein and D.S. Fisher, Boson localization and the superfluid-insulator transition, Phys. Rev. B 40 (1989) 546 [INSPIRE].
J. Williamson, On the algebraic problem concerning the normal forms of linear dynamical systems, Amer. J. Math. 58 (1936) 141.
D. Polarski and A.A. Starobinsky, Semiclassicality and decoherence of cosmological perturbations, Class. Quant. Grav. 13 (1996) 377 [gr-qc/9504030] [INSPIRE].
G.W. Gibbons and S.W. Hawking, Cosmological event horizons, thermodynamics and particle creation, Phys. Rev. D 15 (1977) 2738 [INSPIRE].
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ArXiv ePrint: 1907.00487
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Khlebnikov, S., Sheoran, A. The first heat: production of entanglement entropy in the early universe. J. High Energ. Phys. 2019, 157 (2019). https://doi.org/10.1007/JHEP11(2019)157
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DOI: https://doi.org/10.1007/JHEP11(2019)157