Effects of gravitational lensing on neutrino oscillation in Hu-Sawicki f(R) gravity

Abstract

Gravitational lensing serves as a powerful probe of compact astrophysical objects and dark matter distributions. As relativistic counterparts to photons, neutrinos experiencing lensing offer a complementary means to investigate the properties of curved spacetimes. This paper studies neutrino oscillations within the spacetime geometry described by the Hu-Sawicki f(R) gravity model, focusing on the modifications induced by gravitational lensing. We calculate the oscillation phases for both radial and non-radial neutrino propagation and derive the corresponding flavor transition probabilities for 2-flavor and 3-flavor scenarios under the weak-field approximation. Our analysis demonstrates that the lensing-affected oscillation probabilities exhibit a clear dependence on the Hu-Sawicki model parameter $λ$ , the neutrino mass hierarchy, and the absolute value of the lightest neutrino mass. Furthermore, extending the analysis beyond the weak-field regime reveals that strong-field gravitational lensing amplifies these effects. These results suggest that measurements of lensed neutrino signals could provide a novel avenue for testing modified gravity models and constraining fundamental neutrino parameters.

Figures (8)

• Figure 1: Illustration of gravitational lensing caused by an Hu-Sawicki $f(R)$ gravity model. $S$ is the source, $D$ is the detector. $b$ is the impact factor, $\delta$ is the deflection angle and $\gamma$ marks the misalignment of the coordinates $(x,y)$ and $(x',y')$. For the original construction of the plot, see Swami:2020qdi and the adapted versions see Chakrabarty:2021bprChakrabarty:2023kldAlloqulov:2024sns.
• Figure 2: Oscillation probability of the two flavor case including the lensing effects of Hu-Sawicki $f(R)$ gravity model under weak-field. The neutrino mixing angle is chosen to be $\alpha=\pi/5$, lightest neutrino mass $m_{l}$ is 0, $r_D=10^8$ km, $r_S=10^5 r_D$, $E_0=10$ MeV, $|\Delta m^2|=10^{-3} \text{ eV}^2$.
• Figure 3: Oscillation probability of the two flavor case including the lensing effects of Hu-Sawicki $f(R)$ gravity model under weak-field . The neutrino mixing angle is chosen to be $\alpha=\pi/6$, lightest neutrino mass $m_{l}$ is 0, $r_D=10^8$ km, $r_S=10^5 r_D$, $E_0=10$ MeV, $|\Delta m^2|=10^{-3} \text{ eV}^2$.
• Figure 4: Oscillation probability of two flavor case $\nu_e\to\nu_\mu$. Top and bottom panel corresponds to normal ordering and inverted ordering, respectively. We vary in each plot the mass of the lowest neutrino, which we donate as $m_1$, from 0 eV(Blue line), 0.01 eV(yellow line) and 0.02eV(green line). The neutrino mixing angle are chosen to be $\alpha=\pi/6$, $r_D=10^8$ km, $r_S=10^5 r_D$, $E_0=10$ MeV, $|\Delta m^2|=10^{-3} \text{ eV}^2$.
• Figure 5: Oscillation probability of the three flavor neutrino (normal ordering). From top to bottom correspond to $\nu_e\to\nu_\mu$, $\nu_e\to\nu_\tau$ and $\nu_\mu\to\nu_\tau$, respectively. $r_D=10^8$ km, $r_S=10^5 r_D$, $E_0=10$ MeV