$f(R)$ cosmology from $q$-theory

From a macroscopic theory of the quantum vacuum in terms of conserved relativistic charges (generically denoted by $q^{(a)}$ with label $a$), we have obtained, in the low-energy limit, a particular type of $f(R)$ model relevant to cosmology. The macroscopic quantum-vacuum theory allows us to distinguish between different phenomenological $f(R)$ models on physical grounds.