86 research outputs found
Torsion as electromagnetism and spin
We show that it is possible to formulate the classical Einstein-Maxwell-Dirac
theory of spinors interacting with the gravitational and electromagnetic fields
as the Einstein-Cartan-Kibble-Sciama theory with the Ricci scalar of the
traceless torsion, describing gravity, and the torsion trace acting as the
electromagnetic potential.Comment: 6 pages; published versio
Cosmology with torsion: An alternative to cosmic inflation
We propose a simple scenario which explains why our Universe appears
spatially flat, homogeneous and isotropic. We use the
Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity which naturally extends
general relativity to include the spin of matter. The torsion of spacetime
generates gravitational repulsion in the early Universe filled with quarks and
leptons, preventing the cosmological singularity: the Universe expands from a
state of minimum but finite radius. We show that the dynamics of the closed
Universe immediately after this state naturally solves the flatness and horizon
problems in cosmology because of an extremely small and negative torsion
density parameter, . Thus the ECKS gravity provides
a compelling alternative to speculative mechanisms of standard cosmic
inflation. This scenario also suggests that the contraction of our Universe
preceding the bounce at the minimum radius may correspond to the dynamics of
matter inside a collapsing black hole existing in another universe, which could
explain the origin of the Big Bang.Comment: 8 pages; published versio
Variational formulation of Eisenhart's unified theory
Eisenhart's classical unified field theory is based on a non-Riemannian
affine connection related to the covariant derivative of the electromagnetic
field tensor. The sourceless field equations of this theory arise from
vanishing of the torsion trace and the symmetrized Ricci tensor. We formulate
Eisenhart's theory from the metric-affine variational principle. In this
formulation, a Lagrange multiplier constraining the torsion becomes the source
for the Maxwell equations.Comment: 7 pages; published versio
Propagating torsion in the Einstein frame
The Einstein-Cartan-Saa theory of torsion modifies the spacetime volume
element so that it is compatible with the connection. The condition of
connection compatibility gives constraints on torsion, which are also necessary
for the consistence of torsion, minimal coupling, and electromagnetic gauge
invariance. To solve the problem of positivity of energy associated with the
torsionic scalar, we reformulate this theory in the Einstein conformal frame.
In the presence of the electromagnetic field, we obtain the
Hojman-Rosenbaum-Ryan-Shepley theory of propagating torsion with a different
factor in the torsionic kinetic term.Comment: 10 pages; published versio
The cosmic snap parameter in f(R) gravity
We derive the expression for the snap parameter in f(R) gravity. We use the
Palatini variational principle to obtain the field equations and regard the
Einstein conformal frame as physical. We predict the present-day value of the
snap parameter for the particular case f(R)=R-const/R, which is the simplest
f(R) model explaining the current acceleration of the universe.Comment: 9 pages; published versio
Gravitation, electromagnetism and cosmological constant in purely affine gravity
The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field,
that has the form of the Maxwell Lagrangian with the metric tensor replaced by
the symmetrized Ricci tensor, is dynamically equivalent to the metric
Einstein-Maxwell Lagrangian, except the zero-field limit, for which the metric
tensor is not well-defined. This feature indicates that, for the
Ferraris-Kijowski model to be physical, there must exist a background field
that depends on the Ricci tensor. The simplest possibility, supported by recent
astronomical observations, is the cosmological constant, generated in the
purely affine formulation of gravity by the Eddington Lagrangian. In this paper
we combine the electromagnetic field and the cosmological constant in the
purely affine formulation. We show that the sum of the two affine (Eddington
and Ferraris-Kijowski) Lagrangians is dynamically inequivalent to the sum of
the analogous (CDM and Einstein-Maxwell) Lagrangians in the
metric-affine/metric formulation. We also show that such a construction is
valid, like the affine Einstein-Born-Infeld formulation, only for weak
electromagnetic fields, on the order of the magnetic field in outer space of
the Solar System. Therefore the purely affine formulation that combines
gravity, electromagnetism and cosmological constant cannot be a simple sum of
affine terms corresponding separately to these fields. A quite complicated form
of the affine equivalent of the metric Einstein-Maxwell- Lagrangian
suggests that Nature can be described by a simpler affine Lagrangian, leading
to modifications of the Einstein-Maxwell-CDM theory for
electromagnetic fields that contribute to the spacetime curvature on the same
order as the cosmological constant.Comment: 17 pages, extended and combined with gr-qc/0612193; published versio
The present universe in the Einstein frame, metric-affine R+1/R gravity
We study the present, flat isotropic universe in 1/R-modified gravity. We use
the Palatini (metric-affine) variational principle and the Einstein
(metric-compatible connected) conformal frame. We show that the energy density
scaling deviates from the usual scaling for nonrelativistic matter, and the
largest deviation occurs in the present epoch. We find that the current
deceleration parameter derived from the apparent matter density parameter is
consistent with observations. There is also a small overlap between the
predicted and observed values for the redshift derivative of the deceleration
parameter. The predicted redshift of the deceleration-to-acceleration
transition agrees with that in the \Lambda-CDM model but it is larger than the
value estimated from SNIa observations.Comment: 11 pages; published versio
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