  As the microscopic structure of the deep relativistic quantum vacuum is
unknown, a phenomenological approach ($q$-theory) has been proposed to describe
the vacuum degrees of freedom and the dynamics of the vacuum energy after the
Big Bang. The original $q$-theory was based on a four-form field strength from
a three-form gauge potential. However, this realization of $q$-theory, just as
others suggested so far, is rather artificial and does not take into account
the fermionic nature of the vacuum. We now propose a more physical realization
of the $q$-variable. In this approach, we assume that the vacuum has the
properties of a plastic (malleable) fermionic crystalline medium. The new
approach unites general relativity and fermionic microscopic (trans-Planckian)
degrees of freedom, as the approach involves both the tetrad of standard
gravity and the elasticity tetrad of the hypothetical vacuum crystal. This
approach also allows for the description of possible topological phases of the
quantum vacuum.
