Re: [Phys-L] cosmology

[John Denker <jsd@av8n.com>]

On 10/9/20 9:16 AM, Anthony Lapinski wrote:

> This came up in my astronomy class. So the big bang happened some 13.8 By
> ago. I thought the size (radius) of the visible universe would be 13.8 Bly.
> But after checking for an updated Hubble constant, I found the size
> (radius) of the universe to be around 46 Bly. Is this due to the expansion
> of the universe? How is this value determined? galaxy redshifts?

Well, it is 100% due to expansion of the universe ...
but it is also 100% sensitive to the legalistic definition
of "visible".

If you start at t=0, the big bang, the universe has expanded by a
factor of infinity since then. So if you want to get a finite number
for the size, you have to choose an event later than that.

One reasonable choice is the time when the universe cooled to the
point where it was no longer a plasma (free electrons and protons)
and became instead a bunch of neutral hydrogen atoms.  This event
is observable in the microwave background radiation.  Before this,
the universe was opaque to radiation, so nothing before that will
be "visible", at least not using optical (or radio) telescopes.

Other choices are possible, but let's not get into that.

===

Then you have to do a tricky red-shift-versus-time calculation to
figure out how far light traveled in the available time.

In particular, recently the redshift has been very small, so if you
want to go /halfway/ to the edge of the visible universe, that's just
half the age of the universe times c.  The same is true for three
quarters.  It's only if you want to go all the way (or very nearly)
to the edge that you need to start worrying about redshifts and the
definition of "visible".