32,394 research outputs found
Cyclic and Ekpyrotic Universes in Modified Finsler Osculating Gravity on Tangent Lorentz Bundles
We consider models of accelerating Universe elaborated for Finsler like
gravity theories constructed on tangent bundles to Lorentz manifolds. In the
osculating approximation, certain locally anisotropic configurations are
similar to those for f(R) gravity. This allows us to generalize a proposal (by
Nojiri, Odintsov and Saez-Gomez, arXiv: 1108.0767) in order to reconstruct and
compare two classes of Einstein-Finsler gravity, EFG, and f(R) gravity theories
using modern cosmological data and realistic physical scenarios. We conclude
that EFG provides inflation, acceleration and little rip evolution scenarios
with realistic alternatives to standard Lambda CDM cosmology. The approach is
based on a proof that there is a general decoupling property of gravitational
field equations in EFG and modified theories which allows us to generate
off-diagonal cosmological solutions.Comment: latex2e, 28 pages, version accepted by CQG, with modifications and
additional explanations and new references requested by referee
Self-Similar Anisotropic Texture Analysis: the Hyperbolic Wavelet Transform Contribution
Textures in images can often be well modeled using self-similar processes
while they may at the same time display anisotropy. The present contribution
thus aims at studying jointly selfsimilarity and anisotropy by focusing on a
specific classical class of Gaussian anisotropic selfsimilar processes. It will
first be shown that accurate joint estimates of the anisotropy and
selfsimilarity parameters are performed by replacing the standard 2D-discrete
wavelet transform by the hyperbolic wavelet transform, which permits the use of
different dilation factors along the horizontal and vertical axis. Defining
anisotropy requires a reference direction that needs not a priori match the
horizontal and vertical axes according to which the images are digitized, this
discrepancy defines a rotation angle. Second, we show that this rotation angle
can be jointly estimated. Third, a non parametric bootstrap based procedure is
described, that provides confidence interval in addition to the estimates
themselves and enables to construct an isotropy test procedure, that can be
applied to a single texture image. Fourth, the robustness and versatility of
the proposed analysis is illustrated by being applied to a large variety of
different isotropic and anisotropic self-similar fields. As an illustration, we
show that a true anisotropy built-in self-similarity can be disentangled from
an isotropic self-similarity to which an anisotropic trend has been
superimposed
Callan-Symanzik-Lifshitz approach to generic competing systems
We present the Callan-Symanzik-Lifshitz method to approaching the critical
behaviors of systems with arbitrary competing interactions. Every distinct
competition subspace in the anisotropic cases define an independent set of
renormalized vertex parts via normalization conditions with nonvanishing
distinct masses at zero external momenta. Otherwise, only one mass scale is
required in the isotropic behaviors. At the critical dimension, we prove: i)
the existence of the Callan-Symanzik-Lifshitz equations and ii) the
multiplicative renormalizability of the vertex functions using the inductive
method. Away from the critical dimension, we utilize the orthogonal
approximation to compute higher loop Feynman integrals, anisotropic as well as
isotropic, necessary to get the exponents and at least up
to two-loop level. Moreover, we calculate the latter exactly for isotropic
behaviors at the same perturbative order. Similarly to the computation in the
massless formalism, the orthogonal approximation is found to be exact at
one-loop order. The outcome for all critical exponents matches exactly with
those computed using the zero mass field-theoretic description renormalized at
nonvanishing external momenta.Comment: 58 pages, RevTex4, no figure
Modified Einstein and Finsler Like Theories on Tangent Lorentz Bundles
We study modifications of general relativity, GR, with nonlinear dispersion
relations which can be geometrized on tangent Lorentz bundles. Such modified
gravity theories, MGTs, can be modeled by gravitational Lagrange density
functionals with generalized/ modified scalar
curvature , trace of matter field tensors and modified
Finsler like generating function . In particular, there are defined
extensions of GR with extra dimensional "velocity/ momentum" coordinates. For
four dimensional models, we prove that it is possible to decouple and integrate
in very general forms the gravitational fields for
-modified gravity using nonholonomic 2+2 splitting
and nonholonomic Finsler like variables . We study the modified motion and
Newtonian limits of massive test particles on nonlinear geodesics approximated
with effective extra forces orthogonal to the four--velocity. We compute the
constraints on the magnitude of extra-accelerations and analyze perihelion
effects and possible cosmological implications of such theories. We also derive
the extended Raychaudhuri equation in the framework of a tangent Lorentz
bundle. Finally, we speculate on effective modelling of modified theories by
generic off-diagonal configurations in Einstein and/or MGTs and Finsler
gravity. We provide some examples for modified stationary (black) ellipsoid
configurations and locally anisotropic solitonic backgrounds.Comment: latex2e, 20 pages; version accepted to IJMPD; changed title and
modifications following requests of refere
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