microtech said:
The reason I find this of interest is that the
H value is said to determine the Universe “radius”
r =
c/
H ≈ 1.3×1026 m ≈
13.9 billion lightyears. Which
should mean, according to NASA/WMAP, that anyone trying to tell you that
“the radius of the observable universe is 46.5 billion lightyears” is full of gas... (Example: Wikipedia’s article (
en.wikipedia.org/wiki/Observable_universe), where the “average Universe density” is cited as
“9.9×10−30 g/cm3 (equivalent to 6 protons in a cubic meter of space)” — the
exact same value reported by NASA/WMAP, in a Universe
vastly larger than what
H (currently) indicates! Wikipedia’s “new math” at work?
No, microtech, they're not full of gas. You just misunderstood.
The issue here is that when describing the expanding universe there is more than one useful definition of radius of the universe, and these get often confused, sometimes by people who should know better. It's not as simple as 'how far the light can travel in the age of the universe', as both the expansion and its changing rate conspire to throw off our everyday conception of distance.There are: the Hubble radius, proper distance to the source at the time of emission, proper distance to the source at the time of reception, particle horizon and cosmic event horizon.
Hubble radius ##c/H_0##, equal to about 14 billion light years (using ~70 km/s/Mpc for Hubble constant), is the distance at which the recession exceeds the speed of light (for the specific time). This value being close to the age of the universe times the speed of light is a coincidence - it wasn't always so in the past, and will further diverge in the far future.
Proper distance to the source at the time of emission (let's call it ##D_{then}##) is how far the source was when the now-observed light was emitted in terms of 'proper distance' - i.e., distance you would measure if you could stop the expansion and walk the distance with a measuring stick.
Taking the farthest observable thing in the universe - the CMBR - as an example, its ##D_{then}## was about 42
million light years.
Proper distance at the time of reception, ##D_{now}## is where the object you see is now in terms of proper distance - again, meaning the distance you'd get if you could stop the expansion and measure it disregarding any further expansion.
The ##D_{now}## of the CMBR, or proper radius of the observable universe, is about 46
billion light years. This is the value used for the radius of the universe in the wikipedia article, as it most closely conforms to our everyday idea of how big something is.
Particle horizon is the proper radius of the observable universe at the time of emission of the observed signal. It's not the same as ##D_{then}## due to the changing rate of expansion - what we see now at distance A, was back then at distance B, but it didn't lie within the particle horizon C back then. It wasn't part of the observable universe.
For example, the CMBR is now 46 billion ly away, at the time of emission it was 42 million ly away, while the particle horizon back then was about 1 million ly. That we can see it now, is only due to the fact that in the past the rate of expansion of the universe was decelerating, which allowed objects initially beyond the particle horizon to be eventually observed.
Cosmic event horizon is the largest proper distance that light emitted at a given time can ever bridge. It is now about 16 billion ly and will asymptotically approach about 16.5 billion ly in the future. It is lower than the current radius of the observable universe due to the accelerating expansion.For more detailed discussion of these distances and misconceptions arising from their misuse read this article:
http://arxiv.org/abs/astro-ph/0310808
This calculator might help you familiarise yourself with the interplay of the aforementioned values, as well as redshift, age and recession velocities:
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
(made as an effort of PF member Jorrie with some help from others; there's a related sticky thread in the cosmology section)