Studies on the SJ vacuum in de Sitter spacetime

• Published in: The journal of high energy physics Vol. 2019; no. 7; pp. 1 - 43
• Main Authors: Surya, Sumati, X, Nomaan, Yazdi, Yasaman K.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2019; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Cosmology of Theories beyond the SM; Elementary Particles; Field theory; High energy physics; Models of Quantum Gravity; Nonperturbative Effects; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity; Relativity Theory; Spacetime; SpaceTime Symmetries; String Theory; SpaceTime Symmetries; Cosmology of Theories beyond the SM; Models of Quantum Gravity; Nonperturbative Effects
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2019)009

A bstract In this work we study the Sorkin-Johnston (SJ) vacuum in de Sitter spacetime for free scalar field theory. For the massless theory we find that the SJ vacuum can neither be obtained from the O (4) Fock vacuum of Allen and Folacci nor from the non-Fock de Sitter invariant vacuum of Kirsten and Garriga. Using a causal set discretisation of a slab of 2d and 4d de Sitter spacetime, we find the causal set SJ vacuum for a range of masses m ≥ 0 of the free scalar field. While our simulations are limited to a finite volume slab of global de Sitter spacetime, they show good convergence as the volume is increased. We find that the 4d causal set SJ vacuum shows a significant departure from the continuum Mottola-Allen α -vacua. Moreover, the causal set SJ vacuum is well-defined for both the minimally coupled massless m = 0 and the conformally coupled massless m = m c cases. This is at odds with earlier work on the continuum de Sitter SJ vacuum where it was argued that the continuum SJ vacuum is ill-defined for these masses. Our results hint at an important tension between the discrete and continuum behaviour of the SJ vacuum in de Sitter and suggest that the former cannot in general be identified with the Mottola-Allen α-vacua even for m > 0.