The Hubble "constant" is typically given in terms of units of km/s/mpc. If you convert the distances to a common measure like meters then they cancel out and you are left with a "rate", as in 1/s. http://astro.berkeley.edu/~mwhite/darkmatter/hubble.html(adsbygoogle = window.adsbygoogle || []).push({});

This value describes the proportional expansion of the universe, such as .001/s, meaning for every second that passes a distance of 1 increases by .001 (for illustration, my numbers are not even ballpark; they're just intelligible - the real value is insanely small). Equivalently a distance d increases by .001d, meaning the final distance is given by d+.001d or d*1.001

In cumulative terms, therefore, a distance d over a time t expands to d*(1+r)^t, where r is the rate (my .001 above). This is a standard exponential growth function.

My question is, using the actual Hubble constant H0, what is the cumulative expansion of a distance of length 1 (units are irrelevant it turns out) since the beginning of the universe. How much has an individual unit of space expanded since the beginning of expansion?

It seems very simple, simplifying to (1+Hubble constant)^(age of the universe), but I can't work with these enormous and enormously small numbers at the same time on my pocket calculator and get results that I can trust.

I guess some part of me is expecting the answer to be "the diameter of the universe" but that would not sit well, as that would connect the speed of light (which defines, together with the age of the universe, the 'diameter' of the visible universe) to the rate of expansion. A much more reasonable answer would be "42" or perhaps something which can be logically connected back to another fundamental constant.

Thank you.

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# Cumulative expansion based on H0 since T = 0

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