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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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