is easy to see that a change of the gauge variable (the choice of its parametrization), which looks like $N=v(\tilde N, a)$ for the isotropic model, together with an additional condition for a new variable $\tilde N$, say, $\tilde N=1$, fixes the gauge condition for $N$: $f(a)=v(1, a)$. It has been shown in [@Shest2] that the choice of parametrization function $v(\tilde N, a)=\tilde N a^{n-3}$ (which is equivalent to the gauge condition $N=a^{n-3}$) results in the equation of state $p=\left(\displaystyle\frac n3-1\right)\varepsilon$, where $n$ can have various values, for example, $n=0$ corresponds to de Sitter false vacuum, $n=4$ corresponds a radiation dominated universe, etc. It confirms that at least in some cases one can simulate a medium with required properties only by means of introducing a suitable parametrization and gauge conditions. Another component of the integrated system, which includes pure gravity, matter fields and the observer, is ghost fields; analyzing its quasi-tensor $T_{\mu(ghost)}^{\nu}$ for a given gauge one can obtain its equation of state. However, the role of ghost fields has not been studied enough.

The BRST charge
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It is known that the Faddeev – Popov effective action possesses a residual global symmetry, the so-called BRST symmetry. In the Lagrangian 