Power Spectrum with Auxiliary Fields in de Sitter Space

We use the auxiliary fields and (excited-) de Sitter solutions to study the standard power spectrum of primordial fluctuations of a scalar field in the early universe. The auxiliary fields are the negative norm solutions of the field equation and as it is shown, with a fixed boundary condition, utilizing these states results in a finite power spectrum without any infinity. The power spectrum is determined by the de Sitter solutions up to some corrections and the space-time symmetry is not broken in this point of view. The modulation to the power spectrum is of order $(\frac{H}{\Lambda})^{2}$, where $H$ is the Hubble parameter and $\Lambda$ is the energy scale, e.g., Planck scale.Comment: 7 pages, Krein discussion and section 3 improved, To appear in European Physical Journal

Conformally invariant wave-equations and massless fields in de Sitter spacetime

Conformally invariant wave equations in de Sitter space, for scalar and vector fields, are introduced in the present paper. Solutions of their wave equations and the related two-point functions, in the ambient space notation, have been calculated. The ``Hilbert'' space structure and the field operator, in terms of coordinate independent de Sitter plane waves, have been defined. The construction of the paper is based on the analyticity in the complexified pseudo-Riemanian manifold, presented first by Bros et al.. Minkowskian limits of these functions are analyzed. The relation between the ambient space notation and the intrinsic coordinates is then studied in the final stage.Comment: 21 pages, LaTeX, some details adde

Conformal linear gravity in de Sitter space

It has been shown that the theory of linear conformal quantum gravity must include a tensor field of rank-3 and mixed symmetry [1]. In this paper, we obtain the corresponding field equation in de Sitter space. Then, in order to relate this field with the symmetric tensor field of rank-2, \K_{\alpha\beta} related to graviton, we will define homomorphisms between them. Our main result is that if one insists \K_{\alpha\beta} to be a unitary irreducible representation of de Sitter and conformal groups it must satisfy a filed equation of order 6, which is obtained.Comment: 10 page

Conformally Invariant "Massless" Spin-2 Field in de Sitter Universe

''Massless'' spin-2 field equation in de Sitter space, which is invariant under the conformal transformation, has been obtained. The frame work utilized is the symmetric rank-2 tensor field of the conformal group. Our method is based on the group theoretical approach and six-cone formalism, initially introduced by Dirac. Dirac's six-cone is used to obtain conformally invariant equations on de Sitter space. The solution of the physical sector of massless spin-2 field (linear gravity) in de Sitter ambient space is written as a product of a generalized polarization tensor and a massless minimally coupled scalar field. Similar to the minimally coupled scalar field, for quantization of this sector, the Krein space quantization is utilized. We have calculated the physical part of the linear graviton two-point function. This two-point function is de Sitter invariant and free of pathological large distance behavior.Comment: 22 page

Auxiliary "massless" spin-2 field in de Sitter universe

For the tensor field of rank-2 there are two unitary irreducible representation (UIR) in de Sitter (dS) space denoted by $\Pi^{\pm}_{2,2}$ and $\Pi^{\pm}_{2,1}$ [1]. In the flat limit only the $\Pi^{\pm}_{2,2}$ coincides to the UIR of Poincar\'e group, the second one becomes important in the study of conformal gravity. In the pervious work, Dirac's six-cone formalism has been utilized to obtain conformally invariant (CI) field equation for the "massless" spin-2 field in dS space [2]. This equation results in a field which transformed according to $\Pi^{\pm}_{2,1}$, we name this field the auxiliary field. In this paper this auxiliary field is considered and also related two-point function is calculated as a product of a polarization tensor and "massless" conformally coupled scalar field. This two-point function is de Sitter invariant.Comment: 16 page