general relativity - What's the meaning of the age of the universe?

I'm not asking about how we worked backward from an expanding universe to the age of the big bang, but rather what is the meaning of time in a near infinitely dense point in the context of general relativity? Wouldn't time flow infinitely slowly for a theoretical (though physically impossible) observer?

Answer

No. The standard metric for cosmology is given by:

$$ds^{2} = - dt^{2} + a(t)^{2}\left(d^{3}{\vec x}^{2}\right)$$

where the term inside the parenthees represents the 3-metric of a homogenous three space. As you can see, there is no difficulty with evaluating the age of the universe:

$$T = \int\sqrt{-g}\,\,x^{a}y^{a}z^{a}\epsilon_{abcd} = \int dt$$

where the integral is evaluated from the time when $a = 0$ to now.