## Neutrino oscillations in gravitational and cosmological backgrounds

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Neutrino oscillations in gravitational and cosmological backgrounds George Koutsoumbas1 · Dimitrios Metaxas1 Received: 20 May 2020 / Accepted: 10 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020

Abstract We use the eikonal approximation in order to calculate the additional phase shift between two neutrino mass eigenstates during their propagation in a background of gravitational wave or scalar perturbations in the flat and the FRW spacetime metric. We comment on the dependence of the results on the characteristics of the perturbations, give some order-of-magnitude estimates, and find that, although small, the resulting phase difference persists for large redshifts, up to the validity of our approximations. Keywords Neutrino oscillations · Gravitational waves

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 2 Eikonal approximation and a gravitational wave background 3 Tensor and scalar perturbations in FRW spacetime . . . . . 4 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1 Introduction The phenomenon of flavor oscillations because of the difference between mass and flavor neutrino eigenstates is well-known and described by quantum field theory and quantum mechanics in terms of the phase difference of the respective wave functions during their propagation in flat spacetime [1–5]. Similar calculations have been done

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Dimitrios Metaxas [email protected] George Koutsoumbas [email protected]

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Department of Physics, National Technical University of Athens, Zografou Campus, 15773 Athens, Greece 0123456789().: V,-vol

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in curved spacetime backgrounds [6–13] and are of great theoretical interest, although the gravitational effects are generally too small to be observed experimentally. Because of the various experimental developments in neutrino physics, and related astrophysical and cosmological observations [14,15], as well as the possible relevance of similar calculations in other early universe processes [16–18], we consider here the oscillations between two neutrino flavors in backgrounds involving scalar and tensor perturbations for the flat and the FRW metric. We start by describing in Sect. 2 the eikonal (WKB) approximation used, first in flat spacetime and then its generalization in curved spacetime, in order to set up our formalism and make contact with previous works. As a first application, we consider a gravitational wave perturbation in a flat background and give some order-of-magnitude estimates for the phase difference, finding an interesting dependence on the frequency of the perturbation and the energy of the respective particles (a similar problem has recent

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