102,867 research outputs found
A covariant and gauge invariant formulation of the cosmological "backreaction"
Using our recent proposal for defining gauge invariant averages we give a
general-covariant formulation of the so-called cosmological "backreaction". Our
effective covariant equations allow us to describe in explicitly gauge
invariant form the way classical or quantum inhomogeneities affect the average
evolution of our Universe.Comment: 12 pages, no figures. Typos corrected, matches version to appear in
JCA
T-duality of -correction to DBI action at all orders of gauge field
By explicit calculations of four-field couplings, we observe that the higher
derivative corrections to the DBI action in flat space-time, can be either in a
covariant form or in a T-duality invariant form. The two forms are related by a
non-covariant field redefinition. Using this observation, we then propose a
non-covariant but T-duality invariant action which includes all orders of
massless fields and has two extra derivatives with respect to the DBI action.Comment: 16 pages, latex file, no figure; v3:minor modification, it appears in
NP
The type N Karlhede bound is sharp
We present a family of four-dimensional Lorentzian manifolds whose invariant
classification requires the seventh covariant derivative of the curvature
tensor. The spacetimes in questions are null radiation, type N solutions on an
anti-de Sitter background. The large order of the bound is due to the fact that
these spacetimes are properly , i.e., curvature homogeneous of order 2
but non-homogeneous. This means that tetrad components of are constant, and that essential coordinates first appear as
components of . Covariant derivatives of orders 4,5,6 yield one
additional invariant each, and is needed for invariant
classification. Thus, our class proves that the bound of 7 on the order of the
covariant derivative, first established by Karlhede, is sharp. Our finding
corrects an outstanding assertion that invariant classification of
four-dimensional Lorentzian manifolds requires at most .Comment: 7 pages, typos corrected, added citation and acknowledgemen
1+3 Covariant Cosmic Microwave Background anisotropies II: The almost - Friedmann Lemaitre model
This is the second of a series of papers extending the 1+3 covariant and
gauge invariant treatment of kinetic theory to an examination of Cosmic
Microwave Background temperature anisotropies arising from inhomogeneities in
the early universe. The first paper dealt with algebraic issues.
Here we derive the mode form of the integrated Boltzmann equations, first,
giving a covariant version of the standard derivation using the mode recursion
relations, second, demonstrating the link to the multipole divergence equations
and finally various analytic ways of solving the resulting equations are
discussed.
A general integral form of solution is obtained for the equations with
Thomson scattering. The covariant Friedmann-Lemaitre multipole form of the
transport equations are found using the covariant and gauge-invariant
generalization of the Peebles and Yu expansion in Thompson scattering time. The
dispersion relations and damping scale are then obtained from the covariant
approach. The equations are integrated to give the covariant and
gauge-invariant equivalent of the canonical scalar sourced anisotropies.
We carry out a simple treatment of the matter dominated free-streaming
projection, slow decoupling, and tight-coupling cases, with the aim both giving
a unified transparent derivation of this range of results and clarifying the
connection between the more usual approaches (for example that of Hu and
Sugiyama) and the treatment for scalar perturbations (for example the treatment
of Challinor and Lasenby).Comment: To appear in Annals of Physic
Scalar field and electromagnetic perturbations on Locally Rotationally Symmetric spacetimes
We study scalar field and electromagnetic perturbations on Locally
Rotationally Symmetric (LRS) class II spacetimes, exploiting a recently
developed covariant and gauge-invariant perturbation formalism. From the
Klein-Gordon equation and Maxwell's equations, respectively, we derive
covariant and gauge-invariant wave equations for the perturbation variables and
thereby find the generalised Regge-Wheeler equations for these LRS class II
spacetime perturbations. As illustrative examples, the results are discussed in
detail for the Schwarzschild and Vaidya spacetime, and briefly for some classes
of dust Universes.Comment: 22 pages; v3 has minor changes to match published versio
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