We suggest a perturbative approach for generic choices for the universe equation of state and introduce a novel framework for studying mass varying neutrinos (MaVaNs) coupled to the dark sector. For concreteness, we examine the coupling between neutr
inos and the underlying scalar field associated with the generalized Chaplygin gas (GCG), a unification model for dark energy and dark matter. It is shown that the application of a perturbative approach to MaVaN mechanisms translates into a constraint on the coefficient of a linear perturbation, which depends on the ratio between a neutrino energy dependent term and scalar field potential terms. We quantify the effects on the MaVaN sector by considering neutrino masses generated by the seesaw mechanism. After setting the GCG parameters in agreement with general cosmological constraints, we find that the squared speed of sound in the neutrino-scalar GCG fluid is naturally positive. In this scenario, the model stability depends on previously set up parameters associated with the equation of state of the universe. Our results suggest that the GCG is a particularly suitable candidate for constructing a stable MaVaN scenario.
The Standard Model extension with additional Lorentz violating terms allows for redefining the equation of motion of a propagating left-handed fermionic particle. The obtained Dirac-type equation can be embedded in a generalized Lorentz-invariance pr
eserving-algebra through the definition of Lorentz algebra-like generators with a light-like preferred axis. The resulting modification to the fermionic equation of motion introduces some novel ingredients to the phenomenological analysis of the cross section of the tritium $beta$-decay. Assuming lepton number conservation, our formalism provides a natural explanation for the tritium $beta$-decay end-point via an effective neutrino mass term without the need of a sterile right-handed state.
