Abstract
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 = mc 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.
Highlights
In this work we study the Sorkin-Johnston (SJ) vacuum in de Sitter spacetime for free scalar field theory
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
Our simulations suggest that the causal set theory (CST) 4d de Sitter SJ vacuum for all masses, while de Sitter invariant, is not equivalent to any of the Mottola-Allen α-vacua
Summary
We begin with a short introduction to the SJ vacuum construction for FSQFT in a general globally hyperbolic, finite volume V region of spacetime (M, g) [2, 3, 7, 12, 22]. Let {uq} be a complete set of modes satisfying the KG equation in (M, g) and orthonormal with respect to the KG symplectic form (or KG “norm”). The field operator can be expressed as a mode expansion with respect to the set {uq}. Are the normalised SJ modes which form an orthonormal set in Im(i∆) with respect to the L2 norm sk, sk = λkδkk s∗k, sk = 0. If the KG modes themselves satisfy the L2 orthonormality condition uq, uq = δqq , u∗q, uq = 0,. A case in point is the 2d causal diamond in Minkowski spacetime where the SJ modes for the massless scalar field are not linear combinations of plane waves, and include an important k dependent constant [7, 23], which is a solution for finite V. A similar conclusion was reached in [12] using the Bogoliubov prescription, and in this simple example, the results seem to be independent of the limiting procedure
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
