163 research outputs found
Two-point Functions and Quantum Fields in de Sitter Universe
We present a theory of general two-point functions and of generalized free
fields in d-dimensional de Sitter space-time which closely parallels the
corresponding minkowskian theory. The usual spectral condition is now replaced
by a certain geodesic spectral condition, equivalent to a precise thermal
characterization of the corresponding ``vacuum''states. Our method is based on
the geometry of the complex de Sitter space-time and on the introduction of a
class of holomorphic functions on this manifold, called perikernels, which
reproduce mutatis mutandis the structural properties of the two-point
correlation functions of the minkowskian quantum field theory. The theory
contains as basic elementary case the linear massive field models in their
``preferred'' representation. The latter are described by the introduction of
de Sitter plane waves in their tube domains which lead to a new integral
representation of the two-point functions and to a Fourier-Laplace type
transformation on the hyperboloid. The Hilbert space structure of these
theories is then analysed by using this transformation. In particular we show
the Reeh-Schlieder property. For general two-point functions, a substitute to
the Wick rotation is defined both in complex space-time and in the complex mass
variable, and substantial results concerning the derivation of Kallen-Lehmann
type representation are obtained.Comment: 51 p, uuencoded, LaTex, epsf, 2 figures include
An alternative to quintessence
We consider a FRW cosmological model with an exotic fluid known as Chaplygin
gas. We show that the resulting evolution of the universe is not in
disagreement with the current observation of cosmic acceleration. The model
predict an increasing value for the effective cosmological constant.Comment: 8 pages, latex. References and a new section adde
Cosmology in GSG
We describe what cosmology looks like in the context of the geometric theory
of gravity (GSG) based on a single scalar field. There are two distinct classes
of cosmological solutions. An interesting feature is the possibility of having
a bounce without invoking exotic equations of state for the cosmic fluid. We
also discuss cosmological perturbation and present the basis of structure
formation by gravitational instability in the framework of the geometric scalar
gravity.Comment: 12 pages, 5 figures, accepted for publication in Phys. Rev.
Tachyons, Scalar Fields and Cosmology
We study the role that tachyon fields may play in cosmology as compared to
the well-established use of minimally coupled scalar fields. We first elaborate
on a kind of correspondence existing between tachyons and minimally coupled
scalar fields; corresponding theories give rise to the same cosmological
evolution for a particular choice of the initial conditions but not for any
other. This leads us to study a specific one-parameter family of tachyonic
models based on a perfect fluid mixed with a positive cosmological constant.
For positive values of the parameter one needs to modify Sen's action and use
the sigma process of resolution of singularities. The physics described by this
model is dramatically different and much richer than that of the corresponding
scalar field. For particular choices of the initial conditions the universe,
that does mimick for a long time a de Sitter-like expansion, ends up in a
finite time in a special type of singularity that we call a "big brake". This
singularity is characterized by an infinite deceleration.Comment: 7 figures. Enlarged discussion of the big brake cosmology.
Continuation of the model clarified. References adde
More about scalar gravity
We discuss a class of models for gravity based on a scalar field. The models
include and generalize the old approach by Nordstr\"om which predated and in
some way inspired General Relativity. The class include also a model that we
have recently introduced and discussed in its cosmological aspects (GSG). We
present here a complete characterisation of the Schwarschild geometry as a
vacuum solution of GSG and sketch a discussion of the first Post-Newtonian
approximation.Comment: 11 pages, 1 figure, accepted for publication in PR
Quantum fluctuations in the open universe
We solve a continuing controversy when dealing with density fluctuations in open Friedman-Robertson-Walker universes, on the physical relevance of a class of exponential modes. We show explicitly and rigorously that these modes enter the expansion of quantum fields. In the maximally symmetric de Sitter case, encountered in inflationary models, they are excited for fields with mass below a critical value. They are seen to be responsible for the breaking of the de Sitter symmetry for a massless field. We provide an exact calculation of the power spectrum for any mass. Our method is free of the divergences that appear in earlier treatments. We extend the construction to a generic open FRW universe
Do supernovae favor tachyonic Big Brake instead de Sitter?
We investigate whether a tachyonic scalar field, encompassing both dark
energy and dark matter-like features will drive our universe towards a Big
Brake singularity or a de Sitter expansion. In doing this it is crucial to
establish the parameter domain of the model, which is compatible with type Ia
supernovae data. We find the 1-sigma contours and evolve the tachyonic sytem
into the future. We conclude, that both future evolutions are allowed by
observations, Big Brake becoming increasingly likely with the increase of the
positive model parameter k.Comment: 8 pages, 6 figures, to be published in the Proceedings of the
Invisible Universe International Conference, Paris, 2009, Ed. J. M. Alimi;
v2: reference
Infinite Infrared Regularization and a State Space for the Heisenberg Algebra
We present a method for the construction of a Krein space completion for
spaces of test functions, equipped with an indefinite inner product induced by
a kernel which is more singular than a distribution of finite order. This
generalizes a regularization method for infrared singularities in quantum field
theory, introduced by G. Morchio and F. Strocchi, to the case of singularites
of infinite order. We give conditions for the possibility of this procedure in
terms of local differential operators and the Gelfand- Shilov test function
spaces, as well as an abstract sufficient condition. As a model case we
construct a maximally positive definite state space for the Heisenberg algebra
in the presence of an infinite infrared singularity.Comment: 18 pages, typos corrected, journal-ref added, reference adde
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