Massless spin-2 field in de Sitter space

Abstract

In this paper, admitting a de Sitter (dS)-invariant vacuum in an indefinite inner product space, we present a Gupta-Bleuler type setting for causal and full dS-covariant quantization of free "massless" spin-2 field in dS spacetime. The term "massless" stands for the fact that the field displays gauge and conformal invariance properties. In this construction, the field is defined rigorously as an operatorvalued distribution. It is covariant in the usual strong sense: U g K(X)U −1 g = K(g.X), for any g in the dS group, where U is associated with the indecomposable representations of the dS group, SO0(1, 4), on the space of states. The theory, therefore, does not suffer from infrared divergences. Despite the appearance of negative norm states in the theory, the energy operator is positive in all physical states and vanishes in the vacuum. * bamba@sss.fukushima-u.ac.jp † sur.rahbardehghan.yrec@iauctb.ac.ir 1 For reviews on the so-called dark energy, see, e.g., [1][2][3][4][5][6][7][8][9][10].3 The compact subgroup of the conformal group SO(2, 4) is determined by SO(2) ⊗ SO(4). Considering E as the eigenvalues of the conformal energy generator of SO(2) and (j 1 , j 2 ) as the (2j 1 + 1)(2j 2 + 1) dimensional representation of SO(4) = SU (2) ⊗ SU (2), the symbols C(E, j 1 , j 2 ) stand for irreducible projective representation of SO(2, 4).

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.]…”

‘Hidden’ symmetry of linearized gravity in de Sitter space

“…The KGB quantization scheme, possessing a rigorous group theoretical content which provides a well-defined meaning of massive and massless dS fields (see [34] and references therein), is a new canonical quantization method based on weaker conditions, which do not prohibit negative norm states in the definition of the field. In this sense, it provides a unified framework to treat gauge and gauge-like quantum field theories in dS space (see [26,40] and references therein). In the KGB context, despite the presence of negative norm sates in the theory, the energy operator is positive in all physical states, and vanishes in the vacuum.…”

Gupta-Bleuler quantization for linearized gravity in de Sitter spacetime

“…Substituting the above recurrence formula into the field equation (14) and writing the tensors φ and K in a completely dS-invariant manner in terms of K (see the details in [8]), the tensor field K reads…”

“…10 Note that, we here follow a similar procedure to what we have done in Ref. [8] in order to solve the field equation (14). 11 The bivector W 1 is transverse, therefore we have ∂ · W 1 =∂ · W 1 .…”