Abstract
We present a quantum field theoretical approach to the vacuum neutrino oscillations in curved space, we analyze the non--trivial interplay between quantum field mixing and field quantization in curved space and derive new oscillation formulae. We compute the formulae explicitly in the spatially flat FLRW metrics for universes dominated by a cosmological constant and by radiation. We evaluate the transition probabilities in the Schwarzschild black hole metric, and we show that the Hawking radiation affects the oscillations of neutrinos. We show that our results are consistent with those of previous analyses when the quantum mechanical limit is considered.
Highlights
Since they were theoretically proposed by Pauli [1], neutrinos have proven to be among the most enigmatic particles in the universe
IV we apply the formalism to some spacetimes of interest, including the spatially flat Friedmann–Lemaitre– Robertson–Walker (FLRW) metric for a radiation-dominated universe and for a cosmological constant-dominated universe, and the Schwarzschild black hole metric, where we show the impact of the Hawking effect on neutrino oscillations; in Sec
We have developed a quantum field theoretical approach to the vacuum neutrino oscillations in curved space, discussing the transition probabilities, and their behavior under changes of mass representation
Summary
Since they were theoretically proposed by Pauli [1], neutrinos have proven to be among the most enigmatic particles in the universe. We compute explicitly the oscillation formulas for two examples of spatially flat Friedmann–Lemaitre– Robertson–Walker (FLRW) spacetimes, corresponding to a cosmological constant-dominated and a radiation– dominated universe respectively The paper is organized as follows: in Sec. II we provide the setting for the description of the mass fields in curved space; in Sec. III we develop field mixing and find the oscillation probabilities in curved spacetime, with a thorough analysis of their features; in Sec. IV we apply the formalism to some spacetimes of interest, including the spatially flat FLRW metric for a radiation-dominated universe and for a cosmological constant-dominated universe, and the Schwarzschild black hole metric, where we show the impact of the Hawking effect on neutrino oscillations; in Sec. V we draw our conclusions
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