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