The geometric and thermodynamic parameters of the Universe are given by Although we have assumed here that the cosmic background is filled with viscous matter, the assumption that H = const results in an exponential scale parameter, Eq. (30). This behavior characterizes the de Sitter space, when Λ = k = 0. ρ and T are finite at small t as given in Fig. 2. Another particular solution for Eq. (12) can be obtained, when assuming that the depen- dence of u on H can be given by the polynomial in Eq. (21) where b$_{1}$ and b$_{2}$ are constants. Some simple calculations show that this form is a solution of the initial equation, Eq. (13), if b$_{2}$ is identical to B in Eq. (23). r and γ have to satisfy the compatibility relation Integrating Eq. (35) results in 9 V. PARTICULAR SOLUTION u = b$_{1}$H 2 + b$_{2}$H, (35) b$_{1}$ = − 3 2 1 + γ 1 − r , (36) b$_{2}$ = 1 rα . (37) r = 2 − γ 2 + γ $_{2}$. (38) H ( t ) = b$_{2}$ exp( − b$_{2}$t ) 1 − b$_{1}$ exp( − b$_{2}$t ) , (39) Π( t ) = − 3 γ 4 α $^{1}$γ 9(2 − γ ) 2 , (33) q ( t ) = − 1 . (34) a ( t ) = a$_{0}$ exp [ 4 α − $^{1}$γ 9(2 − γ ) t ] , (30) ρ ( t ) = 3 [ 4 α − $^{1}$γ 9(2 − γ ) ] 2 , (31) T ( t ) = 3 $^{r}$β [ 4 α − $^{1}$γ 9(2 − γ ) ] 2 r , (32)