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If $1 / H_0 $ is about 14 billion years, then what happened when the universe was half its current age?

Is the empirically determined $H_0$ supposed to have been twice its current value?

And when the universe is twice its current age is Hubble's parameter half its current value?

That would predict expansion is slowing. But expansion is actually speeding up. That implies that $ H_0 $ is getting larger, and because $1 / H_0 $ gets smaller in that case, the universe is growing younger.

I asked this question already here, but it was marked a duplicate. I know that Hubble's Parameter is not a constant. That doesn't actually clarify the answers to these questions.

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MikeHelland
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    If you edit your earlier question to explain why the answers to the linked duplicate aren't sufficient, then you can get it reopened. But don't just make the same post all over again. – David Z Oct 24 '13 at 00:18
  • The instructions say "or ask a new question." Thats what I did. Was 1 / H_0 equal to 7 billion years when the universe was half its age? – MikeHelland Oct 24 '13 at 00:24
  • Ah, sorry about the confusion, but you're meant to pay more attention to the part that says you should edit. See this. The point remains that you should never repost the exact same thing you've already posted. – David Z Oct 24 '13 at 00:41
  • @mikethematrix Left a comment sketching an answer on your old question. The short answer is no, not exactly. $H$ is determined by the Friedmann equation in terms of the energy density of the universe. It has nothing directly to do with the age. You should think of $1/H$ as an order of magnitude estimate of the age at best. I completely fails far into the future when the vacuum energy dominates. – Michael Oct 24 '13 at 00:49
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    Is $1 / H_0 $ as the age of the universe today of 14 billion years a coincidence if it doesn't work at 7 billion or 21 billion years? – MikeHelland Oct 24 '13 at 18:51

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