G (?) Del Class Of Approximate Solution Of The Model Of The Universe

In this paper, present status of the modern cosmology is briefly reviewed, that is including the developing process of the standard cosmology from big bang model and Inflation to the quantum model of the universe. It shows that, the standard cosmology model is a relatively perfect universe model for all aspects, and specially, it can trustfully illustrate cosmological red shift, background radiation and element proportion etc. Such the situation, not only means the model has superiority to the other, that can not be replaced, but also the research on the modern cosmology becomes gradually mature. However, we should also see that, several unresolved questions still exist in this cosmology, for example, the so-called question of cosmological constant, that is one of the most mysterious and of the most profound issues. It is almost all people engaged in basic physics research who are facing the most difficult challenge; and the universe grows out of nothing with the aid of the inflation is only one, that can not rule out the other possibility. For the reason, K.Godel developed the Godel cosmological model with the rotational symmetry, which containing the cosmological constantλ, can accurately satisfy the field equations of general relativity. Specially, it should be pointed that, the Godel cosmological model also obtained a non-physical closed spacetime world-line, and this surprising result against the cause-effect law, causes people's interest greatly.The focal point of the paper is studying the evolution behavior of Godel universe in the approximate situation. Particularly, through considering the weak-rotation condition, we will investigate the evolution properties of the universe filled with static ideal fluid and no pressure dust respectively, and correspondingly, the solutions to Einstein field equations are obtained. The result shows that, the expanding ratio of Godel universe is dependent of the matter densityρ, i.e. cosmological scale factorλ. This is consistent with observed phenomenon of the galaxy spectrum red shift and brightness of Ia Type supernovae.