How can we know the time frames for events in the early universe? I just finished watching Into the Universe with Stephen Hawking (2010). Specifically the third episode titled 'The Story of Everything.'
In the episode Hawking is explaining the mainstream theories of the events just after the Big Bang. What confuses me is that he just said at the beginning that the laws of physics were different and time (among other things) did not exist as we know it during this early stage in the life of the universe, but then goes on to say certain events took certain amounts of time.
I don't know if the numbers match, but the same issue exists on this Wikipedia article.
How can we even guess the time frames of these events if time itself is largely dependent on the current state of the universe?
 A: When you see the history of the universe plotted against time, the time used is the comoving time i.e. the time measured by a clock that is at rest with respect to the universe around it. This is the time co-ordinate used in the FLRW metric, which is a solution to the equations of GR that, as far as we can tell, gives a good description of the universe back to very early times.  
Earlier than around the Planck time after the Big Bang we expect the notion of time to become imprecise because it isn't possible to measure times shorter than the Planck time. Without a working theory of quantum gravity it isn't possible to comment further. However for all times later than the Planck time we expect time to be a good co-ordinate and be well behaved. This allows physicists to calculate at what time the various stages in the evolution of the universe happened.
Response to comment
Let me attempt to phrase my answer more broadly. The first point is that in relativity (both Special and General) you need to be careful talking about time. For example you've probably heard that time runs more slowly when you move at speeds near the speed of light. However there is a well defined standard time that cosmologists use for describing the history of the universe. We call this comoving time. So when you hear statements like "the universe is 13.7 billion years old" we mean it's 13.7 billion years old in comoving time. You don't need to know how comoving time is defined, just that it gives us a good timescale for describing the history of the universe back to the Planck time. Which brings us to ...
You've probably also heard of Heisenberg's uncertainty principle. Again I'll gloss over the details, but one side effect of the uncertainty principle is that it's impossible to measure times less than about 5 $\times$ 10$^{-44}$ seconds. I don't know of a simple way to explain this to someone who isn't familiar with quantum mechanics, so I'm afraid you'll have to take this on faith.
And this brings us back to Hawking's programme. As long as the times we are interested in are greater than 5 $\times$ 10$^{-44}$ seconds we can define the time using comoving time so we can assign reliable times to cosmological events like the electroweak transition. But for times close to 5 $\times$ 10$^{-44}$ seconds the whole notion of a "time when something happens" becomes meaningless because it's fundamentally impossible to measure times that short. I'd guess this is what Hawking means when he says time ceases to exist.
