13.7 billion years is a common estimate for the age of the universe. As far as I know this number is calculated using observations of red shifted galaxies. We see that the universe is expanding and simply extrapolate backwards to determine that matter comes to a singularity at T-13.7 billion years. But I wonder if this simple calculation from the "outside" point of view truly represents the proper time a given particle would experience. According to general relativity, time slows down for a particle in a gravity well. For example clocks on GPS satellites run faster than ground based clocks and this effect must be compensated for. Wouldn't this effect be significant in the early dense universe? It occurs to me that the proper time experienced by a particle might be significantly more than 13.7 billion years. Perhaps it even approaches infinity as the universe becomes infinitely dense. Indeed this might change that status of the Big Bang from an actual event to an asymptotic limit.

I am merely an amateur throwing stones here. I would be grateful for expert information on this.