I How big and how old is the Universe?

[Bandersnatch]

I did a search of one of the forums a few weeks ago and found an old post (but I can't find it now of course) that gave the radius of the 3-sphere as:

$R = c / (H_0 sqrt(Ω_K))$

Plugging in the upper limit for $Ω_K$ from the Plank 2015 results then gives a minimum total volume. However, I've seen other sites that use that same argument but get very different numerical values from what I worked out.

You should get the minimum radius of the curvature approx R=205 Gly. Is that what you have?

 

[GeorgeDishman]

You should get the minimum radius of the curvature approx R=205 Gly. Is that what you have?

Yes, for a Hubble Length of 14.4 Gly from Wikipedia: $R = 14.4 / \sqrt(0.005) = 203 Gly$ for the radius, which I think means $2 \pi R = 1280 Gly$ for the circumference (proper distance to return to your starting point) and $2 \pi ^2 R^3 = 1.67*10^6 Gly^3$ total volume. The Planck value is 95% confidence (from memory) so that would be 97.5% confidence minimum limits (50% chance of curvature < 0) assuming a 3-sphere rather than some other topology.

I found the other similar calculation I saw recently by Ethan Siegel in a blog (obviously not an authoritative source) but that seems to be a factor of 10 larger:

"If the Universe does curve back and close on itself, its radius of curvature is at least 150 times as large as the part that’s observable to us! Meaning that — even without speculative physics like cosmic inflation — we know that the entire Universe extends for at least 14 trillion light years in diameter, including the part that’s unobservable to us today."

http://scienceblogs.com/startswithabang/2012/07/18/how-big-is-the-entire-universe/

 

[GeorgeDishman]

In the meantime, you could use these graphs:

Thanks, I recognise those from the Lineweaver paper. The example I gave is outside our cosmological event horizon so the light will never reach us.

 

[Bill McKeeman]

I do not think we have any evidence of what an observer somewhere else in the Universe would see. You must be applying the Cosmological Principal, which is an assumption, not a fact.

 

[PeterDonis]

I do not think we have any evidence of what an observer somewhere else in the Universe would see.

Sure we do; everything we can see is evidence about what observers elsewhere in the universe would see. It's not perfect evidence, but it's not no evidence either.

 

[rootone]

I do not think we have any evidence of what an observer somewhere else in the Universe would see. You must be applying the Cosmological Principal, which is an assumption, not a fact.

I'd say it's a reasonable assumption though, given that all of the Universe which we actually do see, is in fact isotropic and homogeneous at the large scale