Symmetric teleparallel gravitational effects on solar neutrino oscillations

Neutrino oscillations probe the quantum gravity interface in unique ways. While gravitational effects on neutrinos are well studied in general relativity and torsion based geometries, the symmetric teleparallel regime where gravity stems solely from non-metricity, with zero curvature and torsion has remained uncharted. In this work, we perform the first analysis of neutrino oscillations in such a spacetime. Using the reduced Kerr metric in coincident gauge for the slowly rotating and weakly gravitating spherical Sun, we derive the Dirac Hamiltonian from the generalized Dirac equation and compute the accumulated phase of neutrino mass eigenstates. There are six free coupling constants in our model. Based on certain observational inputs, we inferred upper bounds on our arbitrary coupling constants. This allowed us to simplify the otherwise cumbersome calculations to some extent. Ultimately, we computed the phase differences that play a crucial role in solar neutrino oscillations and analyzed the contributions arising from our arbitrary coupling constants. Our results establish neutrino oscillations as a novel probe of non-metricity and open a new avenue for testing symmetric teleparallel gravity through astrophysical observations.

💡 Research Summary

This paper presents the first systematic study of solar neutrino oscillations within the framework of symmetric teleparallel gravity (STPG), a metric‑affine theory in which curvature and torsion vanish while non‑metricity remains the sole source of gravitation. The authors adopt the coincident gauge, in which the affine connection can be set to zero, thereby simplifying calculations without discarding the physical content of non‑metricity.

The Sun is modeled as a slowly rotating, weakly gravitating sphere described by a linearized Kerr metric restricted to the equatorial plane. In this “reduced Kerr” background the tetrad fields and their inverses are explicitly constructed, allowing the authors to compute the symmetric part of the connection (the non‑metricity 1‑form Q_{ab}) and its trace Q as well as the derived 1‑form P.

A generalized Dirac equation appropriate for metric‑affine spacetimes is employed. The spinor covariant derivative contains, besides the usual Lorentz‑generator term σ^{ab}ω_{