Abstract. In the Lagrangian framework for symmetries and conserva-tion laws of field theories, we investigate globality properties of conserved currents associated with non–global Lagrangians admitting global Euler– Lagrange morphisms.... more
Abstract. In the Lagrangian framework for symmetries and conserva-tion laws of field theories, we investigate globality properties of conserved currents associated with non–global Lagrangians admitting global Euler– Lagrange morphisms. Our approach is based on the recent geometric for-mulation of the calculus of variations on finite order jets of fibered manifolds in terms of variational sequences. 1. Introduction. In
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ABSTRACT General Relativity and Standard Model are formulated in terms of scale-invariant variables where the initial data are integrals of motion. In this case, the Hubble law can be explained by a cosmological evolution of particle... more
ABSTRACT General Relativity and Standard Model are formulated in terms of scale-invariant variables where the initial data are integrals of motion. In this case, the Hubble law can be explained by a cosmological evolution of particle masses. Supernovae type Ia data and the CMB energy budget in the model are in agreement with the dominance of a scalar field kinetic energy density and an intensive cosmological creation of primordialW, Z, and Higgs bosons from vacuum. Some arguments are discussed testifying to that two-photon processes of primordial particle annihilation and decays form three peaks in the CMB power spectrum, and their values and positions ℓ = 220, 546, 800 are in agreement with the QED coupling constant,Weinberg’s angle, and the Higgs particle mass of about 118 GeV. PACS numbers95.30.Sf-98.80.-k-98.80.Es
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We demonstrate that the coproduct of and quantum -Poincaré algebras in a classical algebra basis cannot be obtained by a cochain twist depending only on Poincaré algebra generators. We also argue that the nonexistence of such a twist does... more
We demonstrate that the coproduct of and quantum -Poincaré algebras in a classical algebra basis cannot be obtained by a cochain twist depending only on Poincaré algebra generators. We also argue that the nonexistence of such a twist does not imply the nonexistence of a universal R-matrix.
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We study noncommutative deformations of the wave equation in curved backgrounds and discuss the modification of the dispersion relations due to noncommutativity combined with curvature of spacetime. Our noncommutative differential... more
We study noncommutative deformations of the wave equation in curved backgrounds and discuss the modification of the dispersion relations due to noncommutativity combined with curvature of spacetime. Our noncommutative differential geometry approach is based on Drinfeld twist deformation, and can be implemented for any twist and any curved background. We discuss in detail the Jordanian twist — giving κ-Minkowski spacetime in flat space — in the presence of a Friedman-Lemaître-Robertson-Walker (FLRW) cosmological background. We obtain a new expression for the variation of the speed of light, depending linearly on the ratio E ph/E LV (photon energy/Lorentz violation scale), but also linearly on the cosmological time, the Hubble parameter and inversely proportional to the scale factor.
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We explain the effect of dark matter (flat rotation curve) using modified gravitational dynamics. We investigate in this context a low energy limit of generalized general relativity with a nonlinear Lagrangian [Formula: see text], where R... more
We explain the effect of dark matter (flat rotation curve) using modified gravitational dynamics. We investigate in this context a low energy limit of generalized general relativity with a nonlinear Lagrangian [Formula: see text], where R is the (generalized) Ricci scalar and n is parameter estimated from SNIa data. We estimate parameter β in modified gravitational potential [Formula: see text]. Then we compare value of β obtained from SNIa data with β parameter evaluated from the best fitted rotation curve. We find β ≃ 0.7 which becomes in good agreement with an observation of spiral galaxies rotation curve. We also find preferred value of Ωm,0 from the combined analysis of supernovae data and baryon oscillation peak. We argue that although amount of "dark energy" (of non-substantial origin) is consistent with SNIa data and flat curves of spiral galaxies are reproduces in the framework of modified Einstein's equation we still need substantial dark matter. For comparis...
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Toy cosmological models based on non-minimal coupling between gravity and scalar dilaton-like field are presented in the framework of Palatini formalism. They have the following property: preceding to a given cosmological epoch is a dark... more
Toy cosmological models based on non-minimal coupling between gravity and scalar dilaton-like field are presented in the framework of Palatini formalism. They have the following property: preceding to a given cosmological epoch is a dark energy epoch with an accelerated expansion. The next (future) epoch becomes dominated by some kind of dark matter.
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We describe Jordanian “nonstandard” deformation of U(osp(1|2)) by employing the twist quantization technique. An extension o f these results to U(osp(1|4)) describing deformed graded D = 4 AdS symmetries and to their super-Poincaré limit... more
We describe Jordanian “nonstandard” deformation of U(osp(1|2)) by employing the twist quantization technique. An extension o f these results to U(osp(1|4)) describing deformed graded D = 4 AdS symmetries and to their super-Poincaré limit is outlined.
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We show that different topologies of a space-time manifold and different signatures of its metric can be encompassed into a single Lagrangian formalism, provided one adopts the first-order (Palatini) formulation and relies on nonlinear... more
We show that different topologies of a space-time manifold and different signatures of its metric can be encompassed into a single Lagrangian formalism, provided one adopts the first-order (Palatini) formulation and relies on nonlinear Lagrangians, that were earlier shown to produce, in the generic case, universality of Einstein field equations and of Komar's energy-momentum complex as well. An example in Relativistic Cosmology is provided.
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We show that different topologies of a space-time manifold and different signatures of its metric can be encompassed into a single Lagrangian formalism, provided one adopts the first-order (Palatini) formulation and relies on nonlinear... more
We show that different topologies of a space-time manifold and different signatures of its metric can be encompassed into a single Lagrangian formalism, provided one adopts the first-order (Palatini) formulation and relies on nonlinear Lagrangians, that were earlier shown to produce, in the generic case, universality of Einstein field equations and of Komar's energy-momentum complex as well. An example in Relativistic Cosmology is provided.