1,210 research outputs found
Gauge Invariant Treatment of the Energy Carried by a Gravitational Wave
Even though the energy carried by a gravitational wave is not itself gauge
invariant, the interaction with a gravitational antenna of the gravitational
wave which carries that energy is. It therefore has to be possible to make some
statements which involve the energy which are in fact gauge invariant, and it
is the objective of this paper to provide them. In order to develop a gauge
invariant treatment of the issues involved, we construct a specific action for
gravitational fluctuations which is gauge invariant to second perturbative
order. Then, via variation of this action, we obtain an energy-momentum tensor
for perturbative gravitational fluctuations around a general curved background
whose covariant conservation condition is also fully gauge invariant to second
order. Contraction of this energy-momentum tensor with a Killing vector of the
background conveniently allows us to convert this covariant conservation
condition into an ordinary conservation condition which is also gauge invariant
through second order. Then, via spatial integration we are able to obtain a
relation involving the time derivative of the total energy of the fluctuation
and its asymptotic spatial momentum flux which is also completely gauge
invariant through second order. It is only in making the simplification of
setting the asymptotic momentum flux to zero that one would actually lose
manifest gauge invariance, with only invariance under those particular gauge
transformations which leave the asymptotic momentum flux zero then remaining.
However, if one works in an arbitrary gauge where the asymptotic momentum flux
is non-zero, the gravitational wave will then deliver both energy and momentum
to a gravitational antenna in a completely gauge invariant manner, no matter
how badly behaved at infinity the gauge function might be.Comment: 13 pages, revtex4. Final version. To appear in Phys. Rev.
Future deceleration due to cosmic backreaction in presence of the event horizon
The present acceleration of the universe leads to the formation of a
cosmological future event horizon. We explore the effects of the event horizon
on cosmological backreaction due to inhomogeneities in the universe. Beginning
from the onset of the present accelerated era, we show that backreaction in
presence of the event horizon causes acceleration to slow down in the
subsequent evolution. Transition to deceleration occurs eventually, ensuring
avoidance of a big rip.Comment: Latex, 5 pages, 2 figures. This version has small changes to match
with the version published in MNRAS: Letter
Construction of the B88 exchange-energy functional in two dimensions
We construct a generalized-gradient approximation for the exchange-energy
density of finite two-dimensional systems. Guided by non-empirical principles,
we include the proper small-gradient limit and the proper tail for the
exchange-hole potential. The observed performance is superior to that of the
two-dimensional local-density approximation, which underlines the usefulness of
the approach in practical applications
Observational Constraints on the Averaged Universe
Averaging in general relativity is a complicated operation, due to the
general covariance of the theory and the non-linearity of Einstein's equations.
The latter of these ensures that smoothing spacetime over cosmological scales
does not yield the same result as solving Einstein's equations with a smooth
matter distribution, and that the smooth models we fit to observations need not
be simply related to the actual geometry of spacetime. One specific consequence
of this is a decoupling of the geometrical spatial curvature term in the metric
from the dynamical spatial curvature in the Friedmann equation. Here we
investigate the consequences of this decoupling by fitting to a combination of
HST, CMB, SNIa and BAO data sets. We find that only the geometrical spatial
curvature is tightly constrained, and that our ability to constrain dark energy
dynamics will be severely impaired until we gain a thorough understanding of
the averaging problem in cosmology.Comment: 6 pages, 4 figure
The Hubble rate in averaged cosmology
The calculation of the averaged Hubble expansion rate in an averaged
perturbed Friedmann-Lemaitre-Robertson-Walker cosmology leads to small
corrections to the background value of the expansion rate, which could be
important for measuring the Hubble constant from local observations. It also
predicts an intrinsic variance associated with the finite scale of any
measurement of H_0, the Hubble rate today. Both the mean Hubble rate and its
variance depend on both the definition of the Hubble rate and the spatial
surface on which the average is performed. We quantitatively study different
definitions of the averaged Hubble rate encountered in the literature by
consistently calculating the backreaction effect at second order in
perturbation theory, and compare the results. We employ for the first time a
recently developed gauge-invariant definition of an averaged scalar. We also
discuss the variance of the Hubble rate for the different definitions.Comment: 12 pages, 25 figures, references added, clarity improved, frame
switching subtlety fixed, results unchanged, v3 minor typos fixe
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