145 research outputs found

### Nonperturbative late time asymptotics for heat kernel in gravity theory

Recently proposed nonlocal and nonperturbative late time behavior of the heat
kernel is generalized to curved spacetimes. Heat kernel trace asymptotics is
dominated by two terms one of which represents a trivial covariantization of
the flat-space result and another one is given by the Gibbons-Hawking integral
over asymptotically-flat infinity. Nonlocal terms of the effective action
generated by this asymptotics might underly long- distance modifications of the
Einstein theory motivated by the cosmological constant problem. New mechanisms
of the cosmological constant induced by infrared effects of matter and graviton
loops are briefly discussed.Comment: 22 pages, LaTeX, final version, to be published in Phys. Rev.

### Quantum Dirac constraints, Ward identities and path integral in relativistic gauge

Quantum Dirac constraints in generic constrained system are solved by
directly calculating in the one-loop approximation the path integral with
relativistic gauge fixing procedure. The calculations are based on the
reduction algorithms for functional determinants extended to gauge theories.
Explicit mechanism of transition from relativistic gauge conditions to unitary
gauges, participating in the construction of this solution, is revealed by the
method of Ward identities.Comment: 12 pages, LaTe

### Goldstone bosons and a dynamical Higgs field

Higgs inflation uses the gauge variant Higgs field as the inflaton. During
inflation the Higgs field is displaced from its minimum, which results in
associated Goldstone bosons that are apparently massive. Working in a minimally
coupled U(1) toy model, we use the closed-time-path formalism to show that
these Goldstone bosons do contribute to the one-loop effective action.
Therefore the computation in unitary gauge gives incorrect results. Our
expression for the effective action is gauge invariant upon using the
background equations of motion.Comment: 27 pages, 2 figures, published version with minor correction

### Quantum geometrodynamics: whence, whither?

Quantum geometrodynamics is canonical quantum gravity with the three-metric
as the configuration variable. Its central equation is the Wheeler--DeWitt
equation. Here I give an overview of the status of this approach. The issues
discussed include the problem of time, the relation to the covariant theory,
the semiclassical approximation as well as applications to black holes and
cosmology. I conclude that quantum geometrodynamics is still a viable approach
and provides insights into both the conceptual and technical aspects of quantum
gravity.Comment: 25 pages; invited contribution for the Proceedings of the seminar
"Quantum Gravity: Challenges and Perspectives", Bad Honnef, Germany, April
200

### Nonlocal action for long-distance modifications of gravity theory

We construct the covariant nonlocal action for recently suggested
long-distance modifications of gravity theory motivated by the cosmological
constant and cosmological acceleration problems. This construction is based on
the special nonlocal form of the Einstein-Hilbert action explicitly revealing
the fact that this action within the covariant curvature expansion begins with
curvature-squared terms. Nonlocal form factors in the action of both quantum
and brane-induced nature are briefly discussed. In particular, it is emphasized
that for certain class of quantum initial value problems nonlocal nature of the
Euclidean action does not contradict the causality of effective equations of
motion.Comment: 13 pages, LaTeX, final version to appear in Phys. Lett.

### Spectral action beyond the weak-field approximation

The spectral action for a non-compact commutative spectral triple is computed
covariantly in a gauge perturbation up to order 2 in full generality. In the
ultraviolet regime, $p\to\infty$, the action decays as $1/p^4$ in any even
dimension.Comment: 17 pages Few misprints correcte

### Non-minimal coupling, boundary terms and renormalization of the Einstein-Hilbert action

A consistent variational procedure applied to the gravitational action
requires according to Gibbons and Hawking a certain balance between the volume
and boundary parts of the action. We consider the problem of preserving this
balance in the quantum effective action for the matter non-minimally coupled to
metric. It is shown that one has to add a special boundary term to the matter
action analogous to the Gibbons-Hawking one. This boundary term modifies the
one-loop quantum corrections to give a correct balance for the effective action
as well. This means that the boundary UV divergences do not require independent
renormalization and are automatically renormalized simultaneously with their
volume part. This result is derived for arbitrary non-minimally coupled matter.
The example of 2D Maxwell field is considered in much detail. The relevance of
the results obtained to the problem of the renormalization of the black hole
entropy is discussed.Comment: 14 pages, latex. More discussion added, the case of 2D Maxwell field
considered in more detail

### Open inflation from quantum cosmology with a strong nonminimal coupling

We propose the mechanism of quantum creation of the open Universe in the
observable range of values of $\Omega$. This mechanism is based on the
no-boundary quantum state with the Hawking-Turok instanton applied to the model
with a strong nonminimal coupling of the inflaton field. We develop the slow
roll perturbation expansion for the instanton solution and obtain a nontrivial
contribution to the classical instanton action. The interplay of this classical
contribution with the loop effects due to quantum effective action generates
the probability distribution peak with necessary parameters of the inflation
stage without invoking any anthropic considerations. In contrast with a similar
mechanism for closed models, existing only for the tunneling quantum state of
the Universe, the observationally justified open inflation originates from the
no-boundary cosmological wavefunction.Comment: 28 pages, LaTe

### Effective equations in quantum cosmology

We develop a general framework for effective equations of expectation values
in quantum cosmology and pose for them the quantum Cauchy problem with
no-boundary and tunneling wavefunctions. Cosmological configuration space is
decomposed into two sectors that give qualitatively different contributions to
the radiation currents in effective equations. The field-theoretical sector of
inhomogeneous modes is treated by the method of Euclidean effective action,
while the quantum mechanical sector of the spatially homogeneous inflaton is
handled by the technique of manifest quantum reduction to gauge invariant
cosmological perturbations. We apply this framework in the model with a big
negative non-minimal coupling, which incorporates a recently proposed low
energy (GUT scale) mechanism of the quantum origin of the inflationary Universe
and study the effects of the quantum inflaton mode.Comment: 33 pages, LaTeX2

### Gravitons in One-Loop Quantum Cosmology: Correspondence Between Covariant and Non-Covariant Formalisms

The discrepancy between the results of covariant and non-covariant one-loop
calculations for higher-spin fields in quantum cosmology is analyzed. A
detailed mode-by-mode study of perturbative quantum gravity about a flat
Euclidean background bounded by two concentric 3-spheres, including
non-physical degrees of freedom and ghost modes, leads to one-loop amplitudes
in agreement with the covariant Schwinger-DeWitt method. This calculation
provides the generalization of a previous analysis of fermionic fields and
electromagnetic fields at one-loop about flat Euclidean backgrounds admitting a
well-defined 3+1 decomposition.Comment: 29 pages, latex, recently appearing in Physical Review D, volume 50,
pages 6329-6337, November 1994. The authors apologize for the delay in
circulating the paper, due to technical problems now fixe

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