The Gupta-Bleuler triplet for vector-spinor gauge field is presented in de Sitter ambient space formalism. The invariant space of field equation solutions is obtained with respect to an indecomposable representation of the de Sitter group. By using the general solution of the massless spin-3 2 field equation, the vector-spinor quantum field operator and its corresponding Fock space is constructed. The quantum field operator can be written in terms of the vector-spinor polarization states and a quantum conformally coupled massless scalar field, which is constructed on Bunch-Davies vacuum state. The two-point function is also presented, which is de Sitter covariant and analytic. * Electronic address: sajad.parsamehr@srbiau.ac.ir

We demonstrate that the linearized Einstein gravity in de Sitter (dS) spacetime besides the evident symmetries also possesses the additional (local) symmetry hµν → hµν + Eµν χ, where Eµν is a spintwo projector tensor and χ is an arbitrary constant function. We argue that an anomalous symmetry associated with this hitherto 'hidden' property of the existing physics is indeed at the origin of 'dS breaking' in linearized quantum gravity.

We elaborate the definition and properties of "massive" elementary systems in the (1 + 3)dimensional Anti-de Sitter (AdS4) spacetime, on both classical and quantum levels. We fully exploit the symmetry group Sp(4, R), that is, the two-fold covering of SO0(2, 3) (Sp(4, R) ∼ SO0(2, 3) × Z2), recognized as the relativity/kinematical group of motions in AdS4 spacetime. In particular, we discuss that the group coset Sp(4, R)/S U(1) × SU(2) , as one of the Cartan classical domains, can be interpreted as a phase space for the set of free motions of a test massive particle on AdS4 spacetime; technically, in order to facilitate the computations, the whole process is carried out in terms of complex quaternions. The (projective) unitary irreducible representations (UIRs) of the Sp(4, R) group, describing the quantum version of such motions, are found in the discrete series of the Sp(4, R) UIRs. We also describe the null-curvature (Poincaré) and non-relativistic (Newton-Hooke) contraction limits of such systems, on both classical and quantum levels. On this basis, we unveil the dual nature of "massive" elementary systems living in AdS4 spacetime, as each being a combination of a Minkowskian-like massive elementary system with an isotropic harmonic oscillator arising from the AdS4 curvature and viewed as a Newton-Hooke elementary system. This matter-vibration duality will take its whole importance in the quantum regime (in the context of the validity of the equipartition theorem) in view of its possible rôle in the explanation of the current existence of dark matter. Contents

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).

We point out a potential relevance between the Krein-Gupta-Bleuler (KGB) vacuum leading to a fully covariant quantum field theory for gravity in de Sitter (dS) spacetime and the observable smallness of the cosmological constant. This may provide a formulation of linear quantum gravity in a framework amenable to developing a more complete theory determining the value of the cosmological constant.