Story of universe : is it possible? Would appreciate your response

As I was thinking about Universe and read about the plank time concept - a thought started troubling me. Is possible that universe is still in its infancy. Is it possible that the core is still in early infancy while the periphery where we live in has aged? This way we still observe constellations and stars moving away from us which according to us is something which happened during the early stages of the universe.

What are your thoughts on this. Do you know of any text which I can refer to pursue more research on this subject.