48 research outputs found
The issue of time in generally covariant theories and the Komar-Bergmann approach to observables in general relativity
Diffeomorphism-induced symmetry transformations and time evolution are
distinct operations in generally covariant theories formulated in phase space.
Time is not frozen. Diffeomorphism invariants are consequently not necessarily
constants of the motion. Time-dependent invariants arise through the choice of
an intrinsic time, or equivalently through the imposition of time-dependent
gauge fixation conditions. One example of such a time-dependent gauge fixing is
the Komar-Bergmann use of Weyl curvature scalars in general relativity. An
analogous gauge fixing is also imposed for the relativistic free particle and
the resulting complete set time-dependent invariants for this exactly solvable
model are displayed. In contrast with the free particle case, we show that
gauge invariants that are simultaneously constants of motion cannot exist in
general relativity. They vary with intrinsic time
Massive spin 2 propagator on de Sitter space
We compute the Pauli-Jordan, Hadamard and Feynman propagators for the massive
metrical perturbations on de Sitter space. They are expressed both in terms of
mode sums and in invariant forms.Comment: 30 pages + 1 eps fi
Type I vacuum solutions with aligned Papapetrou fields: an intrinsic characterization
We show that Petrov type I vacuum solutions admitting a Killing vector whose
Papapetrou field is aligned with a principal bivector of the Weyl tensor are
the Kasner and Taub metrics, their counterpart with timelike orbits and their
associated windmill-like solutions, as well as the Petrov homogeneous vacuum
solution. We recover all these metrics by using an integration method based on
an invariant classification which allows us to characterize every solution. In
this way we obtain an intrinsic and explicit algorithm to identify them.Comment: 14 pages; v2: added new section, references and tabl
Naturalness in Cosmological Initial Conditions
We propose a novel approach to the problem of constraining cosmological
initial conditions. Within the framework of effective field theory, we classify
initial conditions in terms of boundary terms added to the effective action
describing the cosmological evolution below Planckian energies. These boundary
terms can be thought of as spacelike branes which may support extra
instantaneous degrees of freedom and extra operators. Interactions and
renormalization of these boundary terms allow us to apply to the boundary terms
the field-theoretical requirement of naturalness, i.e. stability under
radiative corrections. We apply this requirement to slow-roll inflation with
non-adiabatic initial conditions, and to cyclic cosmology. This allows us to
define in a precise sense when some of these models are fine-tuned. We also
describe how to parametrize in a model-independent way non-Gaussian initial
conditions; we show that in some cases they are both potentially observable and
pass our naturalness requirement.Comment: 35 pages, 8 figure
On the algebraic classification of spacetimes
We briefly overview the Petrov classification in four dimensions and its
generalization to higher dimensions.Comment: Submitted to Journal of Physics, conference series, proceedings of
4th meeting on constrained dynamics and quantum gravity, 12-16 September
2005, Sardinia, Ital
Holographic dark matter and dark energy with second order invariants
One of the main goals of modern cosmology remains to summon up a self
consistent policy, able to explain, in the framework of the Einstein's theory,
the cosmic speed up and the presence of Dark Matter in the Universe.
Accordingly to the Holographic principle, which postulates the existence of a
minimal size of a physical region, we argue, in this paper, that if this size
exists for the Universe and it is accrued from the independent geometrical
second order invariants, it would be possible to ensure a surprising source for
Dark Matter and a viable candidate for explaining the late acceleration of the
Universe. Along the work, we develop low redshift tests, such as Supernovae Ia
and kinematical analysis complied by the use of Cosmography and we compare the
outcomes with higher redshift tests, such as CMB peak and anisotropy of the
cosmic power spectrum. All the results indicate that the models presented here
can be interpreted as unified models that are capable to describe both the dark
matter and the dark energy.Comment: 12 figures, revtex styl
Curvature invariants in type N spacetimes
Scalar curvature invariants are studied in type N solutions of vacuum
Einstein's equations with in general non-vanishing cosmological constant
Lambda. Zero-order invariants which include only the metric and Weyl (Riemann)
tensor either vanish, or are constants depending on Lambda. Even all
higher-order invariants containing covariant derivatives of the Weyl (Riemann)
tensor are shown to be trivial if a type N spacetime admits a non-expanding and
non-twisting null geodesic congruence.
However, in the case of expanding type N spacetimes we discover a
non-vanishing scalar invariant which is quartic in the second derivatives of
the Riemann tensor.
We use this invariant to demonstrate that both linearized and the third order
type N twisting solutions recently discussed in literature contain
singularities at large distances and thus cannot describe radiation fields
outside bounded sources.Comment: 17 pages, to appear in Class. Quantum Gra
Group theoretical approach to quantum fields in de Sitter space I. The principal series
Using unitary irreducible representations of the de Sitter group, we
construct the Fock space of a massive free scalar field.
In this approach, the vacuum is the unique dS invariant state. The quantum
field is a posteriori defined by an operator subject to covariant
transformations under the dS isometry group. This insures that it obeys
canonical commutation relations, up to an overall factor which should not
vanish as it fixes the value of hbar. However, contrary to what is obtained for
the Poincare group, the covariance condition leaves an arbitrariness in the
definition of the field. This arbitrariness allows to recover the amplitudes
governing spontaneous pair creation processes, as well as the class of alpha
vacua obtained in the usual field theoretical approach. The two approaches can
be formally related by introducing a squeezing operator which acts on the state
in the field theoretical description and on the operator in the present
treatment. The choice of the different dS invariant schemes (different alpha
vacua) is here posed in very simple terms: it is related to a first order
differential equation which is singular on the horizon and whose general
solution is therefore characterized by the amplitude on either side of the
horizon. Our algebraic approach offers a new method to define quantum field
theory on some deformations of dS space.Comment: 35 pages, 2 figures ; Corrected typo, Changed referenc
All spacetimes with vanishing curvature invariants
All Lorentzian spacetimes with vanishing invariants constructed from the
Riemann tensor and its covariant derivatives are determined. A subclass of the
Kundt spacetimes results and we display the corresponding metrics in local
coordinates. Some potential applications of these spacetimes are discussed.Comment: 24 page
Reparameterization invariants for anisotropic Bianchi I cosmology with a massless scalar source
Intrinsic time-dependent invariants are constructed for classical, flat,
homogeneous, anisotropic cosmology with a massless scalar material source.
Invariance under the time reparameterization-induced canonical symmetry group
is displayed explicitly.Comment: 28 pages, to appear in General Relativity and Gravitation.
Substantial revisions: added foundational overview section 2, chose new
intrinsic time variable, worked with dimensionless variables, added appendix
with comparison and criticism of other approache