125502364
Free Embedding Potentials in General Relativity
12564971
Multi-Lagrangians, hereditary operators and Lax pairs for the Korteweg–de Vries positive and negative hierarchies
We present an approach to the construction of action principles (the inverse problem of the calculus of variations), for first order (in time derivatives) differential equations, and generalize it to field theory in order to construct systematically, for integrable equations which are based on the existence of a Nijenhuis (or hereditary) operator, a (multi-Lagrangian) ladder of action principles which is complementary to the well-known multi-Hamiltonian formulation. We work out results for the Korteweg–de Vries (KdV) equation, which is a member of the positive hierarchy related to a hereditary operator. Three negative hierarchies of (negative) evolution equations are defined naturally from the hereditary operator as well, in a concise way, suitable for field theory. The Euler–Lagrange equations arising from the action principles are equivalent to deformations of the original evolution equation, and the deformations are obtained explicitly in terms of the positive and negative evolution vectors. We recogni...
118840558
Neutrino decays over cosmological distances and the implications for neutrino telescopes
We discuss decays of ultra-relativistic neutrinos over cosmological distances by solving the decay equation in terms of its redshift dependence. We demonstrate that there are significant conceptual differences compared to more simplified treatments of neutrino decay. For instance, the maximum distance the neutrinos have traveled is limited by the Hubble length, which means that the common belief that longer neutrino lifetimes can be probed by longer distances does not apply. As a consequence, the neutrino lifetime limit from supernova 1987A cannot be exceeded by high-energy astrophysical neutrinos. We discuss the implications for neutrino spectra and flavor ratios from gamma-ray bursts as one example of extragalactic sources, using up-to-date neutrino flux predictions. If the observation of SN 1987A implies that ν1 is stable and the other mass eigenstates decay with rates much smaller than their current bounds, the muon track rate can be substantially suppressed compared to the cascade rate in the region IceCube is most sensitive to. In this scenario, no gamma-ray burst neutrinos may be found using muon tracks even with the full scale experiment, whereas reliable information on high-energy astrophysical sources can only be obtained from cascade measurements. As another consequence, the recently observed two cascade event candidates at PeV energies will not be accompanied by corresponding muon tracks.
15651666
Extreme scenarios of new physics in the UHE astrophysical neutrino flavour ratios
We add an energy-independent Hamiltonian to the standard flavour oscillation one. This kind of physics might appear in theories where neutrinos couple differently to a plausible non-zero torsion of the gravitational field or more dramatically in the presence of CPT-violating physics in the flavour oscillations. If this contribution exists, experiments at higher energies are more sensitive to their free parameters, and flavour conversion could be severely modified. We show that this new physics modifies the neutrino mixing angles and find expressions that relate the new, effective, angles to the standard oscillation parameters Δm2ij, θij and δC P and to the parameters in the new-physics Hamiltonian, within a three-neutrino formalism. We consider scenarios where the new parameters allow for extreme deviations of the expected neutrino flavour ratios at Earth from their standard values. We show that large departures of the standard flavour scenario are plausible, which would be a strong hint of the violation of a conserved symmetry.