the quantity $ b_{\mu} $, one can obtain the following leading-order expression for its effective value: $$\left( b_{\rm eff} \right)_{\mu} =
        b_{\mu} -
        {{\textstyle}\frac{1}{4}} {\partial}^{\alpha} \chi^{\beta \gamma} \epsilon_{\alpha \beta \gamma \mu} +
        {{\textstyle}\frac{1}{8}} T^{\alpha \beta \gamma} \epsilon_{\alpha \beta \gamma \mu}.$$ Here $ \chi_{\mu a} $ is the antisymmetric part of the vierbein fluctuation against the Minkowski space-time background and $ T^{\lambda}{}_{\mu \nu}$ is the torsion tensor of the Riemann-Cartan space-time (for more detail, see [@Kostelecky_liv_grav] and references therein). Thus, global space-time curvature and possible torsion of the Universe obviously lead to the effects similar to those of the spontaneous Lorentz invariance breaking, so that they may interfere in a peculiar way enhancing or cancelling each other (see also [@Shapiro_liv_grav]). Moreover, a mechanism generating similar effects of Lorentz invariance violation involving chiral fermions has also been proposed [@liv_from_chiral_fermions]. Anyway, in general, since the Lagrangian (\[theory\_L\]) and the experimental bounds on the SME-specific coefficients of the extended QED are actually model-independent (they are derived using the standard quantum field theory techniques), the origin of these coefficients does not affect the way we are going to investigate the model and examine the phenomena arising, provided that the effective Lorentz-violating parameters remain constant in 