84 research outputs found
Exact solutions of the Einstein equations for an infinite slab with a constant energy density
We find exact static solutions of the Einstein equations in the spacetime
with plane symmetry, where an infinite slab with finite thickness and
homogeneous energy (mass) density is present. In the first solution the
pressure is isotropic, while in the second solution the tangential components
of the pressure are equal to zero. In both cases the pressure vanishes at the
boundaries of the slab. Outside the slab these solutions are matched with the
Rindler spacetime and with the Weyl-Levi-Civita spacetime, which represent
special cases of the Kasner solution.Comment: Final version, published in Physics Letters
Future soft singularities, Born-Infeld-like fields and particles
We consider different scenarios of the evolution of the universe, where the
singularities or some non-analyticities in the geometry of the spacetime are
present, trying to answer the following question: is it possible to conserve
some kind of notion of particle corresponding to a chosen quantum field present
in the universe when the latter approaches the singularity? We study scalar
fields with different types of Lagrangians, writing down the second-order
differential equations for the linear perturbations of these fields in the
vicinity of a singularity. If both independent solutions are regular, we
construct the vacuum state for quantum particles as a Gaussian function of the
corresponding variable. If at least one of two independent solutions has a
singular asymptotic behavior, then we cannot define the creation and the
annihilation operators and construct the vacuum. This means that the very
notion of particle loses sense. We show that at the approaching to the Big Rip
singularity, particles corresponding to the phantom scalar field driving the
evolution of the universe must vanish, while particles of other fields still
can be defined. In the case of the model of the universe described by the
tachyon field with a special trigonometric potential, where the Big Brake
singularity occurs, we see that the (pseudo) tachyon particles do not pass
through this singularity. Adding to this model some quantity of dust, we
slightly change the characteristics of this singularity and tachyon particles
survive. Finally, we consider a model with the scalar field with the cusped
potential, where the phantom divide line crossing occurs. Here the particles
are well defined in the vicinity of this crossing point.Comment: 13 pages, 1 figure. Final version to be published in PR
Question of quantum equivalence between Jordan frame and Einstein frame
In the framework of a general scalar-tensor theory, we investigate the
equivalence between two different parametrizations of fields that are commonly
used in cosmology - the so-called Jordan frame and Einstein frame. While it is
clear that both parametrizations are mathematically equivalent at the level of
the classical action, the question about their mathematical equivalence at the
quantum level as well as their physical equivalence is still a matter of debate
in cosmology. We analyze whether the mathematical equivalence still holds when
the first quantum corrections are taken into account. We explicitly calculate
the one-loop divergences in both parametrizations by using the generalized
Schwinger-DeWitt algorithm and compare both results. We find that the quantum
corrections do not coincide off shell and hence induce an off shell dependence
on the parametrization. According to the equivalence theorem, the one-loop
divergences should however coincide on shell. For a cosmological background, we
show explicitly that the on shell equivalence is indeed realized by a
nontrivial cancellation.Comment: 18 pages, 1 figure, revised version accepted for publication in
Physical Review D, new title, section V, VI and VIII of previous arXiv
version removed, references update
One-loop divergences for gravity non-minimally coupled to a multiplet of scalar fields: calculation in the Jordan frame. I. The main results
Using the generalized Schwinger-DeWitt technique, we calculate the divergent
part of the one-loop effective action for gravity non-minimally coupled to a
multiplet of scalar fields. All the calculations are consistently done in the
Jordan frame.Comment: revised version, to appear in Phys. Rev.
Non-minimal Higgs Inflation and Frame Dependence in Cosmology
We investigate a very general class of cosmological models with scalar fields
non-minimally coupled to gravity. A particular representative in this class is
given by the non-minimal Higgs inflation model in which the Standard Model
Higgs boson and the inflaton are described by one and the same scalar particle.
While the predictions of the non-minimal Higgs inflation scenario come
numerically remarkably close to the recently discovered mass of the Higgs
boson, there remains a conceptual problem in this model that is associated with
the choice of the cosmological frame. While the classical theory is independent
of this choice, we find by an explicit calculation that already the first
quantum corrections induce a frame dependence. We give a geometrical
explanation of this frame dependence by embedding it into a more general field
theoretical context. From this analysis, some conceptional points in the long
lasting cosmological debate: "Jordan frame vs. Einstein frame" become more
transparent and in principle can be resolved in a natural way.Comment: 4 pages, 3 figures. To appear in the proceedings of the Multiverse
and Fundamental Cosmology Conference (Multicosmofun 2012), Szczecin, Polan
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