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I read that one second after the big bang the universe was composed of photons electrons and neutrinos. Wouldn't the density of energy/matter have caused such extreme time dilation that the universe would never expand?

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Time dilation only applies between distant observers. Local observers always say that time goes normally around THEM. It's only when separated observers compare each other that you get a problem. So, not, there is no contradiction in having an observer in an arbitrarily dense area say that his local neighborhood is expanding.

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  • $\begingroup$ How about for an observer of the big bang? $\endgroup$
    – user36093
    Jan 13, 2014 at 14:18
  • $\begingroup$ @user36093: there are two senses in which to answer this question. The first is that the big bang is a singularity, so any questions about the big bang itself are outside the realm of applicability of classical general relativity -- every quntity is infinite there, so doing physics there doesn't mean anything. The second answer is to note that every observer in a Robertson-Walker spacetime has the big bang in their past, so in a sense, all of us are observers of the big bang. $\endgroup$ Jan 13, 2014 at 15:46
  • $\begingroup$ nice answer, thanks, but is it assumed that gravity was not active shortly after the big bang? Because otherwise, surely if you have gravity you have GR $\endgroup$
    – user36093
    Jan 19, 2014 at 23:48
  • $\begingroup$ @user36093: yes, of course you have GR, but there's a certain point where the matter density becomes large enough that QFT effects become as significant as the effects of classical GR, and you need a theory which includes both GR and QFT as limits, and this theory has not been rigorously proven to exist. $\endgroup$ Jan 20, 2014 at 0:40

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