Constraints on $f(T)$ Gravity from Solar Neutrino Conversion

We report new constraints on the parameters of $f(T)$ teleparallel gravity, derived from its imprints on neutrino flavor oscillations. Our analysis reveals that the presence of spacetime torsion can alter both vacuum oscillations and the matter enhanced Mikheyev Smirnov Wolfenstein (MSW) resonance. By using data from solar neutrino experiments: Super-Kamiokande, SNO, Borexino, and KamLAND, we perform a combined analysis to place the first direct observational bounds on the neutrino-torsion coupling and $f(T)$ parameters. These results establish neutrino phenomenology as a novel astrophysical probe for testing fundamental modifications of gravity.

💡 Research Summary

The paper investigates how extensions of teleparallel gravity, specifically the f(T) class of theories where the torsion scalar T is promoted to a function f(T)=T+αT², affect solar neutrino flavor oscillations. In teleparallel gravity, gravitation is encoded in spacetime torsion rather than curvature, and the authors work with a “good” tetrad that yields a non‑vanishing torsion vector Tμ while the axial torsion Aμ vanishes for the spherically symmetric configurations considered.

First, the authors solve the field equations in the weak‑field limit (|A(r)|,|B(r)|≪1) for both vacuum and a realistic solar interior modeled by a polynomial density profile. The metric potentials A(r) and B(r) acquire corrections proportional to the parameter α, leading to modified expressions for the torsion scalar T(r) and the only non‑zero component of the torsion vector, T¹(r). In vacuum the solutions reduce to the Schwarzschild metric plus α‑dependent terms; inside the Sun the solutions contain additional contributions from the matter distribution but retain the same α‑dependence at leading order.

Next, the Dirac equation for neutrinos is extended to include a torsion‑neutrino coupling term κVγμTμ. For Dirac neutrinos this vector coupling is allowed, while for Majorana neutrinos the vector current vanishes and only an axial coupling (which is zero here because Aμ=0) could appear. The modified Dirac equation can be interpreted as propagation in an external vector potential Vμ=κVTμ. Consequently, the neutrino phase acquires an extra term Δφtorsion=∫κVT¹dx, and the effective Hamiltonian governing flavor evolution receives a torsion‑induced contribution that modifies both the vacuum oscillation frequency (Δm²/2E) and the matter potential that drives the Mikheyev‑Smirnov‑Wolfenstein (MSW) resonance. The authors derive analytic expressions for the altered oscillation probability Pα→β(E) that incorporate the torsion corrections to the mixing angles and effective mass‑squared differences.

The phenomenological part of the work confronts these theoretical predictions with solar neutrino data from Super‑Kamiokande, SNO, Borexino, and KamLAND. Using the measured electron‑neutrino survival probabilities across the ⁸B, ⁷Be, and pp fluxes, the authors construct a χ² function that depends on the two new parameters α (characterizing the deviation from TEGR) and κV (the strength of the neutrino‑torsion vector coupling). By performing a combined fit they obtain 95 % confidence limits |α|≲10⁻⁴ km² and |κV|≲5×10⁻⁹ eV⁻¹. These bounds are tighter than those derived from classic solar‑system tests of teleparallel gravity and represent the first direct observational constraints on torsion effects in neutrino propagation.

Finally, the paper discusses the implications of these results. The analysis demonstrates that torsion can leave observable imprints on neutrino flavor conversion, providing a novel astrophysical probe of modified gravity. The derived limits on α and κV constrain the parameter space of f(T) models that aim to explain cosmic acceleration without dark energy. The authors also forecast that upcoming high‑precision experiments such as JUNO, DUNE, and Hyper‑Kamiokande could improve the sensitivity to α and κV by one to two orders of magnitude, potentially revealing or further restricting torsion‑induced new physics. The work opens the door to applying similar methods to other environments where neutrinos traverse strong gravitational fields, such as supernovae or the vicinity of black holes, thereby linking neutrino phenomenology, torsion‑based gravity, and cosmology.