  In this work, a microscopic quantum mechanical model for gravitationally
induced decoherence introduced by Blencowe and Xu is investigated in the
context of neutrino oscillations. The focus is on the comparison with existing
phenomenological models and the physical interpretation of the decoherence
parameters in such models. The results show that for neutrino oscillations in
vacuum gravitationally induced decoherence can be matched with phenomenological
models with decoherence parameters of the form $\Gamma_{ij}\sim \Delta
m^4_{ij}E^{-2}$. When matter effects are included, the decoherence parameters
show a dependence on matter effects, which vary in the different layers of the
Earth, that can be explained with the form of the coupling between neutrinos
and the gravitational wave environment inspired by linearised gravity.
Consequently, in the case of neutrino oscillations in matter, the microscopic
model does not agree with many existing phenomenological models that assume
constant decoherence parameters in matter, and their existing bounds cannot be
used to further constrain the model considered here. The probabilities for
neutrino oscillations with constant and varying decoherence parameters are
compared and it is shown that the deviations can be up to 10%. On a theoretical
level, these different models can be characterised by a different choice of
Lindblad operators, with the model with decoherence parameters that do not
include matter effects being less suitable from the point of view of linearised
gravity.
