Since the universe is infinitely old, you should see some very old stars. According to the big bang theory the universe is only 13 billion years old. No stars should be older than 13 billion years. In our cosmology, stars older than this should exist. So we are on the lookout for very old stars. We made some observations [a year ago] which we are still trying to explain but the simplest explanation seems to be that there stars that are 20 billion years old.

Jayant Narlikar's Cosmology