Torsional Effects in the Coupling between Gravity and Spinors -- Yukawa Gravity

TL;DR

This paper investigates how fermionic spin coupling to gravity via torsion can generate massive gravity effects, potentially explaining dark matter and dark energy phenomena through spin-induced modifications of spacetime.

Contribution

It introduces a model where fermion spin-torsion coupling leads to massive gravity and cosmological effects, offering an alternative explanation for dark matter and dark energy.

Findings

Fermionic spin currents generate torsion that breaks Lorentz symmetry.

Gravity acquires a mass due to spin-torsion coupling, affecting cosmological dynamics.

Majorana neutrinos contribute to dark energy and dark matter through their gravitational interactions.

Abstract

We study spinors in the framework of general relativity, starting from the Dirac field Lagrangian in the approximation of weak gravity. We focus on how fermions couple to gravity through the spin connection, and we analyze these couplings by analogy with the Ginzburg-Landau model and the Yukawa interaction known from the Higgs mechanism. By solving the field equations, we explore how these couplings affect the spacetime metric. In particular, torsion generated by fermionic spin currents naturally emerges and leads to the breaking of Lorentz symmetry. As a consequence, gravity acquires a mass and fermions gain additional mass contributions through their interaction with this gravitational field. These effects are localized and diminish quickly with distance. Our model offers an alternative explanation to phenomena usually attributed to dark matter and dark energy. We link these cosmological effects to chirality-flip processes of Majorana neutrinos interacting with a massive graviton. Right-handed Majorana neutrinos, which are sterile under Standard Model interactions, generate repulsive gravitational curvature and act as a source of dark energy, while left-handed neutrinos contribute to attractive gravitational effects akin to dark matter. The spin-gravity coupling modifies the curvature of spacetime, influencing galaxy rotation, the accelerated expansion of the universe, and the bending of light. In short, the intrinsic spin of fermions, when coupled to gravity via torsion, changes gravity from a long-range, massless force to a short-range, massive one. This new framework provides fresh insights into fundamental physics and cosmology, potentially explaining dark matter and dark energy phenomena through spin-related gravitational effects.