Chris L Peterson wrote:
[…] Paul Schlyter wrote:
On Wed, 02 Jan 2019 15:16:41 -0700, Chris L Peterson
wrote:
The diameter of the 4D sphere whose surface we're on is 13.8 billion
years. The diameter of the 3D sphere that defines the observable
universe (a section of the surface of the 4D sphere) is about 93
billion light years, which reflects its increase in size over 13.8
billion light travel years.

Then it has expanded at (90-13.8)/13.8 times the light speed.

Nothing constrains the speed of expansion of the Universe.

Correct, because the expansion is described by *general* relativity, which
loosens the speed limit to be the *local* speed of light (from which the
*coordinate* speed is independent). In the words of Lawrence M. Krauss,
“Space can do whatever the hell it wants.”

Indeed, the edge of the observable universe is simply defined by the distance
beyond which the expansion relative to our position is greater than c.

No, that is a (common?) misconception. You can already see that this cannot
be true if you apply Hubble’s Law and compare the result with your previous
statement:

Regions of space that are receding faster from us (i.e., an arbitrary
observer inside our universe, assuming isotropic expansion) than c are
outside the (observer’s) *Hubble sphere* instead, whose radius R is only
approximately

v_rec = H₀ D Hubble’s Law

v_rec = c
→ D = R = c/H₀ ≈ 1.397 × 10¹⁰ ly,

assuming a Hubble constant H₀ = H(t₀) = 70 (km/s)/Mpc. (Whereas you stated
implicitly and correctly that the radius of the observable universe would be
about 4.65 × 10¹⁰ ly.)

However, as the Hubble parameter H(t) = ̇a(t)∕a(t), with a(t) the scale
factor [a(t₀) = 1], is *NOT* constant as the expansion is *accelerating*,
the Hubble sphere is expanding as well (see above), and it is physically
possible that light emitted beyond the *current* Hubble sphere enters it in
the future; so the Hubble sphere is NOT an event horizon either.

That is why the observable universe is much larger than the Hubble sphere.
The actual event horizon is the particle horizon instead. (cf. Davis &
Lineweaver 2003; URI in the other subthread.)

Every point in the Universe has its own observable universe.

Yes. Also note that there are estimates that our entire universe is up
to (10¹⁰⁰)¹⁰⁰ times larger than the observable one.

I would strongly suggest discussing cosmology outside of a newsgroup
dedicated to *amateur* astronomy, and in a newsgroup where experts are
reading, like sci.astro or sci.physics.relativity, as I cannot see how
that pertains (in its details) to the topic of *amateur* astronomy.

--
PointedEars

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