3,759 research outputs found
Nonsingular Promises from Born-Infeld Gravity
Born-Infeld determinantal gravity formulated in Weitzenbock spacetime is
discussed in the context of Friedmann-Robertson-Walker (FRW) cosmologies. It is
shown how the standard model big bang singularity is absent in certain
spatially flat FRW spacetimes, where the high energy regime is characterized by
a de Sitter inflationary stage of geometrical character, i.e., without the
presence of the inflaton field. This taming of the initial singularity is also
achieved for some spatially curved FRW manifolds where the singularity is
replaced by a de Sitter stage or a big bounce of the scale factor depending on
certain combinations of free parameters appearing in the action. Unlike other
Born-Infeld-like theories in vogue, the one here presented is also capable of
deforming vacuum general relativistic solutions.Comment: 5 pages, no figures. Accepted for publication in Physical Review
Letter
Primordial brusque bounce in Born-Infeld determinantal gravity
We study a particular exact solution to the Born-Infeld determinantal gravity
consisting of a cosmological model which undergoes a brusque bounce. The latter
consists of an event characterized by a non-null (but finite) value of the
squared Hubble rate occurring at a minimum (non-null) scale factor. The energy
density and pressure of the fluid covering the whole manifold are perfectly
well behaved in such an event, but the curvature invariants turn out to be
undefined there because of the undefined character of the time derivative of H.
It is shown that the spacetime results geodesically complete and singularity
free, and that it corresponds to a picture of an eternal Universe in which a
(somewhat unconventional) bounce replaces the standard Big Bang singularity.
This example tends to emphasize that, beyond Einstein's theory of General
Relativity, and in the context of extended theories of gravity formulated by
purely torsional means, the criterion of a singularity based on pathologies of
scalars constructed upon the Riemann curvature tensor, becomes objectionable.Comment: 8 pages, one figure. Typos corrected, some references added and
updated. Final version to appear in Phys. Rev.
Remnant group of local Lorentz transformations in f(T) theories
It is shown that the extended teleparallel gravitational theories, known as
f(T) theories, inherit some on shell local Lorentz invariance associated with
the tetrad field defining the spacetime structure. We discuss some enlightening
examples, such as Minkowski spacetime and cosmological
(Friedmann-Robertson-Walker and Bianchi type I) manifolds. In the first case,
we show that the absence of gravity reveals itself as an incapability in the
selection of a preferred parallelization at a local level, due to the fact that
the infinitesimal local Lorentz subgroup acts as a symmetry group of the frame
characterizing Minkowski spacetime. Finite transformations are also discussed
in these examples and, contrary to the common lore on the subject, we conclude
that the set of tetrads responsible for the parallelization of these manifolds
is quite vast and that the remnant group of local Lorentz transformations
includes one and two dimensional Abelian subgroups of the Lorentz group.Comment: 10 pages. Minor changes. To appear in PR
Non trivial frames for f(T) theories of gravity and beyond
Some conceptual issues concerning theories --a family of modified
gravity theories based on absolute parallelism-- are analyzed. Due to the lack
of local Lorentz invariance, the autoparallel frames satisfying the field
equations are evasive to an \emph{a priori} physical understanding. We
exemplify this point by working out the vierbein (tetrad) fields for closed and
open Friedmann-Robertson-Walker cosmologies.Comment: 7 pages, 3 figures, some references added. Accepted for publication
in Phys. Lett. B. Final Versio
A type of Born-Infeld regular gravity and its cosmological consequences
Born-Infeld deformation strategy to smooth theories having divergent
solutions is applied to the teleparallel equivalent of General Relativity. The
equivalence between teleparallelism and General Relativity is exploited to
obtain a deformed theory of gravity based on second order differential
equations, since teleparallel Lagrangian is built just from first derivatives
of the vierbein. We show that Born-Infeld teleparallelism cures the initial
singularity in a spatially flat FRW universe; moreover, it provides a natural
inflationary stage without resorting to an inflaton field. The Born-Infeld
parameter bounds the dynamics of Hubble parameter H(t) and establishes a
maximum attainable spacetime curvature.Comment: 3 pages. Talk given at the 7th Alexander Friedmann International
Seminar on Gravitation and Cosmology, Joao Pessoa, Brazil, July 200
Born-Infeld Determinantal gravity and the taming of the conical singularity in 3-dimensional spacetime
In the context of Born-Infeld \emph{determinantal} gravity formulated in a
n-dimensional spacetime with absolute parallelism, we found an exact
3-dimensional \emph{vacuum} circular symmetric solution without cosmological
constant consisting in a rotating spacetime with non singular behavior. The
space behaves at infinity as the conical geometry typical of 3-dimensional
General Relativity without cosmological constant. However, the solution has no
conical singularity because the space ends at a minimal circle that no freely
falling particle can ever reach in a finite proper time. The space is curved,
but no divergences happen since the curvature invariants vanish at both
asymptotic limits. Remarkably, this very mechanism also forbids the existence
of closed timelike curves in such a spacetime.Comment: 6 pages, 2 figures. References added, some discussions improved.
Version accepted in Phys. Lett.
Spherically symmetric static spacetimes in vacuum f(T) gravity
We show that Schwarzschild geometry remains as a vacuum solution for those
four-dimensional f(T) gravitational theories behaving as ultraviolet
deformations of general relativity. In the gentler context of three-dimensional
gravity, we also find that the infrared-deformed f(T) gravities, like the ones
used to describe the late cosmic speed up of the Universe, have as the
circularly symmetric vacuum solution a Deser-de Sitter or a BTZ-like spacetime
with an effective cosmological constant depending on the infrared scale present
in the function f(T).Comment: 8 pages. Some typos corrected and references updated. One additional
typo corrected in Eq. (33). Accepted for publication in Physical Review D.
Final versio
Local symmetries in -like models: lessons from 2D
The comprehension of the intricate structure associated to the local
symmetries encoded in the tetrad field, as well as its physical meaning, is
perhaps the most important unsolved problem within gravity. This is
inextricably connected to the number, nature and potential impact that the
additional degree/s of freedom might have within these --and other closely
related--models of gravity in which the local Lorentz invariance is broken at
some level. Here we review and further explain some recent results which make
use of the more placid scenery provided by 2D-torsional models of gravity,
where the local symmetries adapted to a given geometry can be fully
characterized.Comment: Contribution to be submitted to the Int. J. Geom. Methods Mod. Phys.
special issue "Metric-Affine Gravity at Tartu
Compact extra dimensions in cosmologies with f(T) structure
The presence of compact extra dimensions in cosmological scenarios in the
context of f(T)-like gravities is discussed. For the case of toroidal
compactifications, the analysis is performed in an arbitrary number of extra
dimensions. Spherical topologies for the extra dimensions are then carefully
studied in six and seven spacetime dimensions, where the proper vielbein fields
responsible for the parallelization process are found.Comment: 11 pages, one figure (added). Typos corrected, manuscript improved.
Additional material is contained in section IV. Accepted for publication in
Physical Review
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