The basic number you hear all the time is that the Hubble expansion rate is(adsbygoogle = window.adsbygoogle || []).push({});

71 km/s per megaparsec

So get the google calculator to tell you want actual percentage growth rate that turns out to be. Say over a billion year span of time. Past this blue thing verbatim into the google window:

71 km/s per megaparsec*10^9 years

That's the approximate fractional growth in a billion years. If you want itin percentthen paste this in the window:

71 km/s per megaparsec*10^9 years in percent

If you don't specify to the calculator in what terms you want the answer, it will say the answer in whatever terms it thinks are appropriate. If you know what terms you want it in, it can help to specify (as we did here.)

Now the expansion rate actually changes gradually over time, so it would be more precise to use a shorter time interval, like a year, or a thousand years, or a million years. But those more precise tactics lead to very small percentage numbers. What we're really talking about is aninstantaneousrate, but for convenience we express it crudely with a billion-year time step.

And 71 is just a commonly used ballpark figure. There is a plus-minus errorbar for it.

You can see from google that it corresponds to about 7 percent increase in distance per billion years. (But I really mean theinstantaneous rate 7 billionthsof a percent per year.)

The actual figure the googleator gives is 7.26. Round it off to 7.3 or 7 if you want.

I will keep using 7.26, and not round off, because it is just an alias for that conventional number 71.

What I want to suggest doing is use this expansion rate of about 7 percent per billion years to estimate the density of the universe (including everything: ordinary and dark).

Corresponding to every density, there is an ideal perfect expansion rate which is just the rate needed so the universe is spatially flat and stays flat.

So conversely, given any particular expansion rate there is a perfect ideal density (the critical density) that is just right so she is spatially flat and stays that way.

What I'm suggesting is that anyone at cosmo forum who hasn't already calculated the critical density (that goes with 7.26 percent expansion) should try it.

And I'll show how. It's easy.

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# *quantitative* fun with the cosmos (easy)

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