Time dilation between now vs right after the Big Bang should imply the universe is much older than 13.8 bn years? The universe is said to be 13.8 bn years old. But if we go back in time towards the Big Bang singularity time will slow down more and more and eventually stop because of the density of the singularity. So why say the universe is 13.8 bn years old? That is from our perspective but in fact the universe must be infinitely old. What do you think?
 A: Time does not speed up or slow down for an observer measuring time on a clock that they carry. The 13.8 billion year age of the universe is the time measured on a clock carried by an observer that is co-moving with the expansion.
There is no problem with a singularity in the same way that the time measured on a clock carried by an observer falling into a black hole is well defined (and finite).
A: Good question.  Now let us suppose that the universe started out with a Big Bang from a single point of singularity.  At that point, time moves at a crawl, or hardly at all, from the perspective of a remote observer. Time starts to move only when the size has somewhat expanded out of the singularity.   So looks like 13.8 billion is an OK figure for such a fictitious remote observer.  I say this because there was no remote observer then!  Suppose a hypothetical person from the singularity is still alive, then the question is whether his or her clock shows 13.8 billion or longer.  Though the fictitious remote observer may see clock of the singularity inhabitant to be almost stopped in the very early stage of expansion, for the person in the singularity the clock always moves normally. Therefore one could say that the universe in reality has no beginning, although the fictitious remote observer, who never existed when the universe started, will continue arguing for a beginning in time.
