In this paper we will make further theoretical analysis for the validity of the accelerating universe based on General Relativity and three new problems of the standard model of the universe are presented from different perspectives. The first part, analyzed the explosion mechanism of the cosmic initial singularity and put forward a different view from the rest. It’s virtually impossible to start with a giant explosion, the big bang by now cosmologists had refined the idea. The second part devised a new model of the twin paradox. It’s one in which people have been consider to include both special and general relativity in the calculations to expose the counterintuitive weirdness of relativity theory. It seems to has a curious coincidence with the cat-a feline in a locked box that is both dead and alive until the box is opened-was a thought experiment devised by physicist Schr ödinger. In part three the author makes determination on the cosmological deceleration parameter q0 by using mathematical derivation, and based on which to construct a thought experiment on cosmological redshift. It is needed to make a static model of the universe that both conforms to the Copernican principle and satisfies Hubble’s law and it’s possible to make us a fresh perspective and thought process.