32 research outputs found
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 , where is the
Hubble parameter and 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 and
[1]. In the flat limit only the 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 , 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