Dynamics In A Maximally Symmetric Universe

Our present understanding of the evolution of the universe relies upon the Friedmann-rnRobertson- Walker cosmological models. This model is so successful that it is now beingrnconsidered as the Standard Model of Cosmology. So in this work we derive the Friedmannrnequations using the Friedmann-Robertson-Walker metric together with Einsteinrn eld equation and then we give a simple method to reduce Friedmann equations to arnsecond order linear di erential equation when it is supplemented with a time dependentrnequation of state. Furthermore, as illustrative examples, we solve this equation for somernspeci c time dependent equation of states. And also by using the Friedmann equationsrnwith some time dependent equation of state we try to determine the cosmic scale factor(thernrate at which the universe expands) and age of the Friedmann universe, for the matterrndominated era, radiation dominated era and for both matter and radiation dominated erarnby considering di erent cases. We have nally discussed the observable quantities thatrncan be evidences for the accelerated expansion of the Friedmann universe

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