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Some remarks on the attractor behaviour in ELKO cosmology
Recent results on the dynamical stability of a system involving the
interaction of the ELKO spinor field with standard matter in the universe have
been reanalysed, and the conclusion is that such system does not exhibit
isolated stable points that could alleviate the cosmic coincidence problem.
When a constant parameter related to the potential of the ELKO field
is introduced in the system however, stable fixed points are found for some
specific types of interaction between the ELKO field and matter. Although the
parameter is related to an unknown potential, in order to satisfy the
stability conditions and also that the fixed points are real, the range of the
constant parameter can be constrained for the present time and the
coincidence problem can be alleviated for some specific interactions. Such
restriction on the ELKO potential opens possibility to apply the ELKO field as
a candidate to dark energy in the universe, and so explain the present phase of
acceleration of the universe through the decay of the ELKO field into matter.Comment: 17 pages, section III with minor changes and section IV rewritten
with a new analysi
Braneworlds scenarios in a gravity model with higher order spatial three-curvature terms
In this work we study a Horava-like five-dimensional model in the context of
braneworld theory. To begin with, the equations of motion of such model are
obtained and, within the realm of warped geometry, we show that the model is
consistent if and only if takes its relativistic value 1.
Furthermore, since the first derivative of the warp factor is discontinuous
over the branes, we show that the elimination of problematic terms involving
the square of the warp factor second order derivatives are eliminated by
imposing detailed balance condition in the bulk. Afterwards, the Israel's
junction conditions are computed, allowing the attainment of an effective
Lagrangian in the visible brane. In particular, for a (4+1)-dimensional
Horava-like model defined in the bulk without cosmological constant, we show
that the resultant effective Lagrangian in the brane corresponds to a
(3+1)-dimensional Horava-like model with an emergent positive cosmological
constant but without detailed balance condition. Now, restoration of detailed
balance condition, at this time imposed over the brane, plays an interesting
role by fitting accordingly the sign of the arbitrary constant that
labels the extra terms in the model, insuring a positive brane tension and a
real energy for the graviton within its dispersion relation. To end up with,
the brane consistency equations are obtained and, as a result, we show that the
detailed balance condition again plays an essential role in eliminating bad
behaving terms and that the model admits positive brane tensions in the
compactification scheme if, and only if, is negative, what is in
accordance with the previous result obtained for the visible brane.Comment: 23 pages, 1 figure, title modifie
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