The neutrino behavior in the Einstein$\text{-}$Hilbert$\text{-}$Bumblebee gravity around global monopole field

TL;DR

The paper analyzes how neutrino oscillations are modified by the Einstein-Hilbert-Bumblebee gravity around a global monopole field. It derives the neutrino oscillation phase in this spacetime, including radial and non-radial null-paths, and presents a lensing-augmented oscillation probability for a two-flavor system, highlighting the roles of the Lorentz-violation parameter $a$ and the global monopole parameter $\bar{\mu}$. The results show that $a$ mainly shifts the oscillation peak while $\bar{\mu}$ and the lightest neutrino mass influence the oscillation frequency; the lensing formalism also introduces dependencies on $\sum m_{ij}^2$ and $\Delta m_{ij}^2$, implying potential sensitivity to absolute neutrino masses. The numerical analysis in a Sun–Earth-like setup demonstrates qualitative differences from Schwarzschild lensing and discusses observational prospects and degeneracies with neutrino masses. Overall, the work suggests curved-spacetime neutrino oscillations could serve as a novel probe of Lorentz-violating gravity and global-monopole effects, complementing other astrophysical tests.

Abstract

In this work, we study the neutrino oscillation phase propagating along radial and non-radial paths in the Einstein$\text{-}$Hilbert$\text{-}$Bumblebee (EHB) gravity around global monopole field, by using the quantummechanical treatment, the expression of the corrected neutrino oscillation probability is obtained. Our results show that neutrino oscillation in the EHB gravity around global monopole field is different from that in Schwarzschild black hole, the Lorentz-violating parameter $a$ mainly affects the peak of the oscillation probability, and the global monopole $\overline { μ}$ and the lightest neutrino mass both affect the frequency of the oscillations of probabilities, which means that studying the neutrino oscillation phenomenon in curved spacetime may not only become a new technology for probing the properties of compact celestial bodies, but also help deepen our understanding of neutrinos.

Figures (6)

• Figure 1: Diagrammatic representation of weak lensing of neutrinos.
• Figure 2: Oscillation probability of gravitationally lensed neutrinos. Values of the parameters are as follows: $M=M_{\odot}$, $\Delta m^2={10}^{-3}{eV}^2$ and the mass of the lightest neutrino is zero.
• Figure 3: Oscillation probability of gravitationally lensed neutrinos. Values of the parameters are as follows:$M=M_{\odot}$, $\Delta m^2={10}^{-3}{eV}^2$ and the mass of the lightest neutrino is zero.
• Figure 4: Effect of the global monopole $\overline { \mu }$ on the oscillation probability. Values of the parameters are as follows:$M=M_{\odot}$, $\Delta m^2={10}^{-3}{eV}^2$ and the mass of the lightest neutrino is zero.
• Figure 5: Effect of the Lorentz-violating parameter $a$ on the oscillation probability. Values of the parameters are as follows:$M=M_{\odot}$, $\Delta m^2={10}^{-3}{eV}^2$ and the mass of the lightest neutrino is zero.