The age of the universe

I was having a science and science history discussion with a relative recently. He is aware that I do not subscribe to the theory of evolution. While talking about atomic theory and cosmology he asked whether I subscribed to a billion year old earth. I informed him that the earth is only 6000 years old to his mild amusement (though we have covered this topic before). He responded by asking if I though the universe was billions of years old. This is a slightly different question.

My response, "According to which reference frame?"

He acknowledged this was a reasonable reply, though the conversation turned elsewhere before I fleshed this out.

If we accept the theory of general relativity is a moderately accurate description of the universe—one I am willing to accept currently, though have little concern about dropping it in favour of alternative theories—then measures of time, and hence age, are relative to the reference frame used.

It is assumed by many that there is no preferred reference frame (cosmological principle), but even if there exists a preferred reference frame, time measurements may be different in other (non-preferred) reference frames. Young earth creationists have made use of this in describing various cosmologies, the only biblical limitation being that the age of the universe is about 6000 years as measured from the earth's reference frame.