Covariant and infrared-free graviton two-point function in de Sitter spacetime

Abstract

In this paper, the two-point function of linearized gravitons on de Sitter (dS) space is presented. Technically, respecting the dS ambient space notation, the field equation is given by the coordinateindependent Casimir operators of the de Sitter group. Analogous to the quantization of the electromagnetic field in Minkowski space, the field equation admits gauge solutions. The notation allows us to exhibit the formalism of Gupta-Bleuler triplets for the present field in exactly the same manner as it occurs for the electromagnetic field. In this regard, centering on the spin-two part (the traceless part, K t ), the field solution is written as a product of a generalized polarization tensor and a minimally coupled massless scalar field. Then, admitting a de Sitter-invariant vacuum through the so-called "Krein space quantization", the de Sitter fully covariant two-point function is calculated. This function is interestingly free of pathological large distance behavior (infrared divergence). Moreover, the spin-zero part (the pure-trace part; K pt ) of the field is discussed in this paper. It is shown that the implications of the dS group unitary irreducible representations restrict the gauge-fixing parameter to the optimal value, which remarkably results in the pure-trace part be written in terms of a conformally coupled massless scalar field.

A small non-vanishing cosmological constant from the Krein–Gupta–Bleuler vacuum

“…Our aim in the present work, instead, will be to point out a potential relevance between the observable smallness of the cosmological constant and a choice of vacuum in the dS gravitational background of * bamba@sss.fukushima-u.ac.jp † Enayati@iauctb.ac.ir ‡ s.rahbardehghan@iauctb.ac.ir our expanding Universe, now known as the KGB vacuum. This vacuum, based on a new representation of the canonical commutation relations, was recently proposed as an alternative to the dS natural vacuum state (the Bunch-Davies state) that yields a fully covariant and coordinate-independent quantization (the KGB quantization) of linearized gravity in dS space [6][7][8][9][10][11][12]. [Due to the lack of the natural dS-invariant vacuum state for free gravitons, the fact that is now widely accepted in the physics community (see, for instance, [7,13,14]), the usual canonical quantization seems to break down for field theory of dS quantum gravity.]…”

Massless spin-2 field in de Sitter space

“…The important point to note here is that Eq. (18) is exactly the ambient counterpart of the transverse-traceless sector of the dS linearized Einstein equation in the context of the most general gauge-fixing functionals [24,25]. It is obvious that the field equation (18) becomes fully gauge invariant if we put c = 1.…”

“…Of course, it is a direct consequence of demanding the full dS covariance of the theory, which unavoidably necessitates negative norm states (the KGB structure). 6 In this construction, therefore, two-point functions and the vacuum are not 6 A straightforward calculation reveals that the only full dScovariant and causal two-point function which naturally appears is the commutator, but it is not of positive type [24,25] (see also [37]).…”

Gupta-Bleuler quantization for linearized gravity in de Sitter spacetime

“…On this basis, we categorize the total space V c (see (30)) as a chain of the solutions, known as the Gupta-Bleuler triplet, in the following form…”