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Register a new userBipartite Riemann-Finsler geometry and Lorentz violation
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Bipartite Riemann-Finsler geometries with complementary Finsler structures are constructed. Calculable examples are presented based on a bilinear-form coefficient for explicit Lorentz violation.
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The correspondence between Riemann-Finsler geometries and effective field theories with spin-independent Lorentz violation is explored. We obtain the general quadratic action for effective scalar field theories in any spacetime dimension with Lorentz-violating operators of arbitrary mass dimension. Classical relativistic point-particle lagrangians are derived that reproduce the momentum-velocity and dispersion relations of quantum wave packets. The correspondence to Finsler structures is established, and some properties of the resulting Riemann-Finsler spaces are investigated. The results provide support for open conjectures about Riemann-Finsler geometries associated with Lorentz-violating field theories.
The physics of classical particles in a Lorentz-breaking spacetime has numerous features resembling the properties of Finsler geometry. In particular, the Lagrange function plays a role similar to that of a Finsler structure function. A summary is presented of recent results, including new calculable Finsler structures based on Lagrange functions appearing in the Lorentz-violation framework known as the Standard-Model Extension.
In this work, we compute some phenomenological bounds for the electromagnetic and massive gravitational high-derivative extensions supposing that it is possible to have an astrophysical process that generates simultaneously gravitational and electromagnetic waves. We present Lorentz invariance violating (LIV) higher-order derivative models, following the Myers-Pospelov approach, to electrodynamics and massive gravitational waves. We compute the corrected equation of motion of these models, their dispersion relations and the velocities. The LIV parameters for the gravitational and electromagnetic sectors, $xi_{g}$ and $xi_{gamma}$, respectively, were also obtained for three different approaches: luminal photons, time delay of flight and the difference of graviton and photon velocities. These LIV parameters depend on the mass scales where the LIV-terms become relevant, $M$ for the electromagnetic sector and $M_{1}$ for the gravitational one. We obtain, using the values for $M$ and $M_{1}$ found in the literature, that $xi_{g}sim10^{-2}$, which is expected to be phenomenologically relevant and $xi_{gamma}sim10^{3}$, which cannot be suitable for an effective LIV theory. However, we show that $xi_{gamma}$ can be interesting in a phenomenological point of view if $Mgg M_{1}$. Finally the relation between the variation of the velocities of the photon and the graviton in relation to the speed of light was calculated and resulted in $Delta v_{g}/Delta v_{gamma}lesssim1.82times 10^{-3}$.
The cosmological evolution of an interacting scalar field model in which the scalar field interacts with dark matter, radiation, and baryon via Lorentz violation is investigated. We propose a model of interaction through the effective coupling $bar{beta}$. Using dynamical system analysis, we study the linear dynamics of an interacting model and show that the dynamics of critical points are completely controlled by two parameters. Some results can be mentioned as follows. Firstly, the sequence of radiation, the dark matter, and the scalar field dark energy exist and baryons are sub dominant. Secondly, the model also allows the possibility of having a universe in the phantom phase with constant potential. Thirdly, the effective gravitational constant varies with respect to time through $bar{beta}$. In particular, we consider a simple case where $bar{beta}$ has a quadratic form and has a good agreement with the modified $Lambda$CDM and quintessence models. Finally, we also calculate the first post--Newtonian parameters for our model.
In this paper, we investigate a novel implication of the non-negligible spacetime curvature at large distances when its effects are expressed in terms of a suitably modified form of the Heisenberg uncertainty relations. Specifically, we establish a one-to-one correspondence between such modified uncertainty principle and the Standard Model Extension (SME), a string-theoretical effective field theory that accounts for both explicit and spontaneous breaking of Lorentz symmetry. This tight correspondence between string-derived effective field theory and modified quantum mechanics with extended uncertainty relations is validated by comparing the predictions concerning a deformed Hawking temperature derived from the two models. Moreover, starting from the experimental bounds on the gravity sector of the SME, we derive the most stringent constraint achieved so far on the value of the free parameter entering in the extended Heisenberg uncertainty principle.
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