0 0.05 0.1 0.15 0.2 0.25 1 1.005 1.015 1.025 1.035 T a FIG. 1: dynamics of scale factor with respect to T terms of the time variable T (Fig.1). Again, We have recovered a monotonic dependence of our new variable T with respect to the isotropic variable of the Universe a and the universe expansion begins with no singularity. In particular, we are more interested to find the behavior of the isotropic variables a and p$_{a}$ when β$_{+}$ = 0 and β − = 0. We find the equations of motions as, The nontrivial solution of the above coupled non linear differential equations (38) and (39), for the scale factor gives where c$_{1}$ and c$_{2}$ are positive constants of integrations. This solution shows that the universe has no singularity at all. Besides, the universe shrinks to a big crunch as T goes to infinity while it reaches a maximum size during its history. Note that, in the isotropic limit, the Bianchi IX model contains the closed FRW model and the behavior of the scale factor a is as expected for this model. a ( T ) = 2 √ c$_{1}$$_{e}$√ $^{c}$1 2 ( T + c$_{2}$ ) (4 c$_{1}$ + e 2 √ c$_{1}$ ( T + c$_{2}$ $^{)}$) 1 2 , (40) P ′ a = − aP 2 a 12 − 6 a $^{3}$. (39) a ′ = a $^{2}$P$_{a}$ 12 , (38) and Isotropic Bianchi type IX : 7