During cosmic inflation, the universe's volume doubles only about 260 times. Not much, but still, if this happens during an amazingly short time duration Δt, it would be an amazingly fast process. Lets see about this. The duration of cosmic inflation Δt is constrained by particle physics. Reheating, which is the end of inflation, also called “Big Bang”, must happen before the so called electro-weak symmetry breaks at around 10-12 seconds in cosmic time.
Cosmic time is here back calculated and expressed relative to a certain, convenient time scale. It does not imply a metaphysical t = 0 moment where time itself was created. Below zero, there may be t < 0 as usual. Before inflation, there may be nothing but a so called “de Sitter phase”, which is in a certain sense the pinnacle of boring as far as exciting space-times go.
All we need to know is that inflation happens somewhere between t = 0 and reheating at t = treheat, and so its duration Δt is about the same size as its endpoint treheat. Alright then, let us assume a small Δt to get a very fast inflation. Let us make it 1020 times faster than the limit from particle physics: After only Δt ~ treheat = 10-32 seconds, inflation is already finished.
The relevant time in fundamental space-time processes is the Planck time tP of about 10-43 s. Therefore we have T/tP = 10-32/10-43 = 10+11 fundamental units of time to accomplish 260 doublings. If we were to imagine fundamental volumes (microscopic boxes of space) multiplying like bacteria, every generation has 1011/260 ~ 109 time steps!
Multiplying E. coli bacteria serve as a toy model of cosmic inflation.
109 human heartbeats are equivalent to about 10 to 100 years. Not exactly bunny speed. And do not forget, we could have assumed Δt much longer, and then 100 years would turn into many times the age of the universe.
Straw-man: “Who knows what the size of the Planck time really is. And you forgot a factor of 2 somewhere. And the picture with the bacteria multiplying – are you some sort of crack pot or what? Cosmic expansion does not expand into an outside space like a culture of bacteria in a Petri dish! Give me string theory or something else I can feel important with in public! And is it or is it not faster than light?”
I will get into all this in the next post.
Painfully Slow Inflation