W^2=\frac{C_2(r)}W+\frac1{C_1^2(r)}-1,$$ $C_2(r)$ is another arbitrary function. The substitution of (\[LTB.sol\]) into (\[eLN3\]) together with (\[eLV3\]) gives the solution for dust energy density $$\label{dust.sol}
\varepsilon=\frac1{8\pi}\frac{C'_2(r)}{W'W^2}.$$

### The Friedmann closed isotropic model.

We can obtain the Einstein equations for the Friedmann closed isotropic model as a particular case of Eqs. (\[eLN1\]) – (\[g.c.1.1\]). We then should put $$\label{isotr.nod}
V(t,r)=a(t),\qquad
W(t,r)=a(t)\sin r.$$ Eq. (\[eLN1\]) gives the constraint $$\label{eLN4}
\frac{a\dot a^2}{N^2}+a=0.$$ Eq. (\[eLNr1\]) is identically satisfied. Eqs. (\[eLV1\]), (\[eLW1\]) are both reduced to the dynamical equation $$\label{eLa4}
\frac{a\ddot a}N+\frac{\dot a^2}{2N}-\frac{a\dot a\dot N}{N^2}+\frac N2=0.$$ Eqs. (\[eLN4\]), (\[eLa4\]) should be complemented by a gauge condition $N=f(a)$, or $$\label{d.c.1.4}
\dot N=\frac{df}{da}\dot a.$$

The same equations can be obtained from the Hamiltonian set (\[DN1\]) – (\[DPW1\]). From (\[DW1\]), (\[DV1\]) we get $$\label{FRW.mom}
P_V=\frac{W\dot W}N=\frac{a\dot a}N \sin^2r,\qquad
P_W=\frac{W\dot V}N+\frac{V\dot W}N=\frac{2a\dot a}N\sin r.$$ Eq. (\[DN1\]) can be rewritten in the form (\[d.c.1.4\]) keeping in mind that $$\label{ch.var}
\frac{df}{da}=\frac{\partial f}{\partial V}+\frac{\partial f}{\partial W}\sin r.$$ Eq. (\[DPN1\]) leads to the constraint (\[eLN4\]). Eq. (\[DPNr1\]) is identically satisfied. Eqs. (\[DPV1\]), (\[DPW1\]) can be both reduced to the equation (\[eLa4\]).

A possible role of gauge-noninvariant terms.
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In this section we shall discuss the role of Lagrange multipliers and ghosts in the extended set 