254 research outputs found
Dynamically generated four-dimensional models in Lovelock cosmology
We consider a class of D-dimensional Lovelock models provided with a positive cosmological constant whose induced metric is given by the product of the metrics of a three-dimensional (external) and a D-4-dimensional (internal) maximally symmetric space. When all the Lovelock coefficients are non-negative, we show that these models admit classical solutions with a constant internal scale factor, and that for these solutions the evolution of the external dimensions can be described by a four-dimensional Einstein theory with a positive effective Hilbert-Einstein coefficient and non-negative effective cosmological constant. In addition, we prove that the perturbative formalism for the treatment of the Lovelock model is always well defined in the region of the gravitational configuration space covered by the considered solutions with a constant internal scale factor. We also examine the dynamically generated four-dimensional theory that is obtained when the internal scale factor remains constant, and discuss the role played by the no-boundary condition in the corresponding process of reducing the degrees of freedom of the minisuperspace model. © 1992 The American Physical Society.Peer Reviewe
Primordial Fluctuations in Loop Quantum Cosmology
Jurekfest 2019 Faculty of Physics, University of Warsaw, Warszawa, Poland,September 16-20, 2019. -- Conference on the occasion of Jerzy Lewandowski's 60th birthday (Jurekfest). -- Presentación con 24 diapositiva
Large quantum gravity effects: Cylindrical waves in four dimensions
Linearly polarized cylindrical waves in four-dimensional vacuum gravity are
mathematically equivalent to rotationally symmetric gravity coupled to a
Maxwell (or Klein-Gordon) field in three dimensions. The quantization of this
latter system was performed by Ashtekar and Pierri in a recent work. Employing
that quantization, we obtain here a complete quantum theory which describes the
four-dimensional geometry of the Einstein-Rosen waves. In particular, we
construct regularized operators to represent the metric. It is shown that the
results achieved by Ashtekar about the existence of important quantum gravity
effects in the Einstein-Maxwell system at large distances from the symmetry
axis continue to be valid from a four-dimensional point of view. The only
significant difference is that, in order to admit an approximate classical
description in the asymptotic region, states that are coherent in the Maxwell
field need not contain a large number of photons anymore. We also analyze the
metric fluctuations on the symmetry axis and argue that they are generally
relevant for all of the coherent states.Comment: Version accepted for publication in Int. J. Mod. Phys.
Lovelock gravity and classical wormholes
The authors first considers Lovelock gravity as a perturbative theory and then apply the results to a D-dimensional homogeneous and isotropic minisuperspace model provided with matter fields for which there exist instanton solutions. He develops a general procedure to analyse these solutions, which may be interpreted as representing tunnelling. Adding some reasonable restrictions to the Lovelock coefficients, it is shown that the Lovelock corrections preserve the essential feature of Einstein gravity models, giving rise to an essentially unique instanton solution. © 1991Peer Reviewe
Involutions on the algebra of physical observables from reality conditions
Some aspects of the algebraic quantization program proposed by Ashtekar are revisited in this article. It is proven that, for systems with first-class constraints, the involution introduced on the algebra of quantum operators via reality conditions can never be projected unambiguously to the algebra of physical observables, i.e., of quantum observables modulo constraints. It is nevertheless shown that, under sufficiently general assumptions, one can still induce an involution on the algebra of physical observables from reality conditions, though the involution obtained depends on the choice of particular representatives for the equivalence classes of quantum observables. © 1996 American Institute of Physics.This work was supported by funds provided by DGICYT and the Spanish Ministry of Education and Science under Contract Adjunct to the Project No. PB91-0052Peer Reviewe
Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology
We study scalar fields subject to an equation of the Klein-Gordon type in
nonstationary spacetimes, such as those found in cosmology, assuming that all
the relevant spatial dependence is contained in the Laplacian. We show that the
field description ---with a specific canonical pair--- and the Fock
representation for the quantization of the field are fixed indeed in a unique
way (except for unitary transformations that do not affect the physical
predictions) if we adopt the combined criterion of (a) imposing the invariance
of the vacuum under the group of spatial symmetries of the field equations and
(b) requiring a unitary implementation of the dynamics in the quantum theory.
Besides, we provide a spacetime interpretation of the field equations as those
corresponding to a scalar field in a cosmological spacetime that is conformally
ultrastatic. In addition, in the privileged Fock quantization, we investigate
the generalization of the evolution of physical states from the hyperbolic
dynamical regime to an elliptic regime. In order to do this, we contemplate the
possibility of processes with signature change in the spacetime where the field
propagates and discuss the behavior of the background geometry when the change
happens, proving that the spacetime metric degenerates. Finally, we argue that
this kind of signature change leads naturally to a phenomenon of particle
creation, with exponential production.Comment: 11 pages, version accepted for publication in Physical Review
The Martin-Benito-Mena Marugan-Olmedo prescription for the Dapor-Liegener model of Loop Quantum Cosmology
Recently, an alternative Hamiltonian constraint for Loop Quantum Cosmology
has been put forward by Dapor and Liegener, inspired by previous work on
regularization due to Thiemann. Here, we quantize this Hamiltonian following a
prescription for cosmology proposed by Mart\'{\i}n-Benito, Mena Marug\'an, and
Olmedo. To this effect, we first regularize the Euclidean and Lorentzian parts
of the Hamiltonian constraint separately in the case of a Bianchi I cosmology.
This allows us to identify a natural symmetrization of the Hamiltonian which is
apparent in anisotropic scenarios. Preserving this symmetrization in isotropic
regimes, we then determine the Hamiltonian constraint corresponding to a
Friedmann-Lema\^itre-Robertson-Walker cosmology, which we proceed to quantize.
We compute the action of this Hamiltonian operator in the volume eigenbasis and
show that it takes the form of a fourth-order difference equation, unlike in
standard Loop Quantum Cosmology, where it is known to be of second order. We
investigate the superselection sectors of our constraint operator, proving that
they are semilattices supported only on either the positive or the negative
semiaxis, depending on the triad orientation. Remarkably, the decoupling
between semiaxes allows us to write a closed expression for the generalized
eigenfunctions of the geometric part of the constraint. This expression is
totally determined by the values at the two points of the semilattice that are
closest to the origin, namely the two contributions with smallest eigenvolume.
This is in clear contrast with the situation found for the standard Hamiltonian
of Loop Quantum Cosmology, where only the smallest value is free. This result
indicates that the degeneracy of the new geometric Hamiltonian operator is
equal to two, doubling the possible number of solutions with respect to the
conventional quantization considered until now.Comment: 15 pages, published in Physical Review
Perturbations in Hybrid Loop Quantum Cosmology: Continuum Limit in Fourier Space
We analyze the passage to a continuum limit of the mode spectrum of
primordial perturbations around flat cosmological spacetimes in hybrid Loop
Quantum Cosmology, showing that this limit can be reached even if one starts by
considering a finite fiducial cell as spatial slice. We focus our attention on
regimes in which the background cosmology follows the effective dynamics of
Loop Quantum Cosmology, although we comment on extensions of our arguments
beyond this regime, as well as to some formalisms other than the hybrid
approach. Whereas the perturbed system can be described in an invariant way
under changes of the fiducial volume using the standard variables of the
improved prescription for Loop Quantum Cosmology, we show that the desired
continuum limit can be established by means of scaling transformations of the
physical volume when this volume grows unboundedly. These transformations lead
to a model with a continuum of modes and independent of any scale of reference
for the physical volume. For the sake of comparison, we also consider an
alternative road to the continuum in Fourier space that has been employed in
geometrodynamics and is based on the use of scaling transformations of the
fiducial volume, together with variables that are independent of them.Comment: 13 page
Length Uncertainty in a Gravity's Rainbow Formalism
It is commonly accepted that the combination of quantum mechanics and general
relativity gives rise to the emergence of a minimum uncertainty both in space
and time. The arguments that support this conclusion are mainly based on
perturbative approaches to the quantization, in which the gravitational
interactions of the matter content are described as corrections to a classical
background. In a recent paper, we analyzed the existence of a minimum time
uncertainty in the framework of doubly special relativity. In this framework,
the standard definition of the energy-momentum of particles is modified
appealing to possible quantum gravitational effects, which are not necessarily
perturbative. Demanding that this modification be completed into a canonical
transformation determines the implementation of doubly special relativity in
position space and leads to spacetime coordinates that depend on the
energy-momentum of the particle. In the present work, we extend our analysis to
the quantum length uncertainty. We show that, in generic cases, there actually
exists a limit in the spatial resolution, both when the quantum evolution is
described in terms of the auxiliary time corresponding to the Minkowski
background or in terms of the physical time. These two kinds of evolutions can
be understood as corresponding to perturbative and non-perturbative
descriptions, respectively. This result contrasts with that found for the time
uncertainty, which can be made to vanish in all models with unbounded physical
energy if one adheres to a non-perturbative quantization.Comment: 12 pages, accepted for publication in Physical Review
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