57 research outputs found
Selection rules for the Wheeler-DeWitt equation in quantum cosmology
Selection of physically meaningful solutions of the Wheeler-DeWitt equation
for the wavefunction in quantum cosmology, can be attained by a reduction of
the theory to the sector of true physical degrees of freedom and their
canonical quantization. The resulting physical wavefunction unitarily evolving
in the time variable introduced within this reduction can then be raised to the
level of the cosmological wavefunction in superspace of 3-metrics. We apply
this technique in several simple minisuperspace models and discuss both at
classical and quantum level physical reduction in {\em extrinsic} time -- the
time variable determined in terms of extrinsic curvature. Only this extrinsic
time gauge can be consistently used in vicinity of turning points and bounces
where the scale factor reaches extremum. Since the 3-metric scale factor is
canonically dual to extrinsic time variable, the transition from the physical
wavefunction to the wavefunction in superspace represents a kind of the
generalized Fourier transform. This transformation selects square integrable
solutions of the Wheeler-DeWitt equation, which guarantee Hermiticity of
canonical operators of the Dirac quantization scheme. Semiclassically this
means that wavefunctions are represented by oscillating waves in classically
allowed domains of superspace and exponentially fall off in classically
forbidden (underbarrier) regions. This is explicitly demonstrated in flat FRW
model with a scalar field having a constant negative potential and for the case
of phantom scalar field with a positive potential. The FRW model of a scalar
field with a vanishing potential does not lead to selection rules for solutions
of the Wheeler-DeWitt equation, but this does not violate Hermiticity
properties, because all these solutions are anyway of plane wave type and
describe cosmological dynamics without turning points and bounces.Comment: final version, to appear in Physical Review
Cosmological Landscape and Euclidean Quantum Gravity
Quantum creation of the universe is described by the {\em density matrix}
defined by the Euclidean path integral. This yields an ensemble of universes --
a cosmological landscape -- in a mixed quasi-thermal state which is shown to be
dynamically more preferable than the pure quantum state of the Hartle-Hawking
type. The latter is suppressed by the infinitely large positive action of its
instanton, generated by the conformal anomaly of quantum matter. The
Hartle-Hawking instantons can be regarded as posing initial conditions for
Starobinsky solutions of the anomaly driven deSitter expansion, which are thus
dynamically eliminated by infrared effects of quantum gravity. The resulting
landscape of hot universes treated within the cosmological bootstrap (the
self-consistent back reaction of quantum matter) turns out to be limited to a
bounded range of the cosmological constant, which rules out a well-known
infrared catastrophe of the vanishing cosmological constant and suggests an
ultimate solution to the problem of unboundedness of the cosmological action in
Euclidean quantum gravity.Comment: 6 pages, to be published in the Special issue of J. Phys. A dedicated
to the Quantum Theories and Renormalization Group in Gravity and Cosmology
(IRGAC 2006, Barcelona, Spain, 11-15 July 2006
Darkness without dark matter and energy -- generalized unimodular gravity
We suggest a Lorentz non-invariant generalization of the unimodular gravity
theory, which is classically equivalent to general relativity with a locally
inert (devoid of local degrees of freedom) perfect fluid having an equation of
state with a constant parameter . For the range of near this dark
fluid can play the role of dark energy, while for this dark dust admits
spatial inhomogeneities and can be interpreted as dark matter. We discuss
possible implications of this model in the cosmological initial conditions
problem. In particular, this is the extension of known microcanonical density
matrix predictions for the initial quantum state of the closed cosmology to the
case of spatially open Universe, based on the imitation of the spatial
curvature by the dark fluid density. We also briefly discuss quantization of
this model necessarily involving the method of gauge systems with reducible
constraints and the effect of this method on the treatment of recently
suggested mechanism of vacuum energy sequestering.Comment: 11 pages, final version, to be published in Physics Letters
Inflation scenario via the Standard Model Higgs boson and LHC
We consider a quantum corrected inflation scenario driven by a generic GUT or
Standard Model type particle model whose scalar field playing the role of an
inflaton has a strong non-minimal coupling to gravity. We show that currently
widely accepted bounds on the Higgs mass falsify the suggestion of the paper
arXiv:0710.3755 (where the role of radiative corrections was underestimated)
that the Standard Model Higgs boson can serve as the inflaton. However, if the
Higgs mass could be raised to GeV, then the Standard Model could
generate an inflationary scenario with the spectral index of the primordial
perturbation spectrum (barely matching present observational
data) and the very low tensor-to-scalar perturbation ratio .Comment: 13 pages, LaTe
On the functional determinant of a special operator with a zero mode in cosmology
The functional determinant of a special second order quantum-mechanical
operator is calculated with its zero mode gauged out by the method of the
Faddeev-Popov gauge fixing procedure. This operator subject to periodic
boundary conditions arises in applications of the early Universe theory and, in
particular, determines the one-loop statistical sum in quantum cosmology
generated by a conformal field theory (CFT). The calculation is done for a
special case of a periodic zero mode of this operator having two roots (nodes)
within the period range, which corresponds to the class of cosmological
instantons in the CFT driven cosmology with one oscillation of the cosmological
scale factor of its Euclidean Friedmann-Robertson-Walker metric.Comment: LaTex, 15 pages, a new section is added, containing the discussion of
a special case of the operator having the second zero mode, typos are
correcte
- …