On Sunday, January 12, 2020 at 9:58:06 AM UTC-6, John Clark wrote:
>
> On Thu, Jan 2, 2020 at 2:30 AM Alan Grayson <[email protected]
> <javascript:>> wrote:
>
>
>> *> If we're convinced it's finite in age, then it can't be infinite in
>> spatial extent. AG *
>
>
> We don't know for sure our universe is infinite in size and we'll never
> know for sure because we'll never be able to measure precisely zero
> curvature with no error at all, but we do know it's pretty damn flat, if
> it's curved it's so slight that a light beam would have to go at least 500
> times as far as our telescopes can see for it to return where it started.
> So if you respect the empirical evidence for the Big Bang but the idea of a
> beginning of a infinitely sized universe makes you unhappy then the
> Multiverse idea offers you an obvious solution, you get an infinitely large
> infinitely old Multiverse but with the observable universe having a
> beginning and being only finitely large. However I understand the
> Multiverse makes you unhappy too. I fear you may be destined to be unhappy.
>
> By the way ... does the inverse also make you unhappy, something
> infinitely old but finite in spatial extent?
>
> John K Clark
>
The expansion factor in the FLRW metric, or approximately the de Sitter
metric, is exp(√{Λ/3}r) for Λ = 10^{-52}m^{-2}. Now for the most early
universe at the Planck scale we think of the expansion fac-tor expanding
the Planck scale ℓ_p = √{Għ/c^3} = 1.6×10^{-35}m to the scale of the
cosmological horizon 10^{10}light years or 10^{26}m. This means (√{Λ/3}r ≈
140 and so the radial distance is 140 times the horizon distance or about
1.9 trillion light years. The CMB is out to 46 billion light years. This is
the absolute furthest we can receive any information from the distant past
observable universe. This would involve gravitational wave or graviton data
on the CMB that originated at the earliest moments. It is possible I think
that we may observe this.
If we can observe this information it might in time be possible to
determine if there is any net curvature to the universe out to this scale.
If no curvature is found we can only say the universe is flat out the to
uncertainty imposed by this fundamental limit on quantum bit information
available. We are fundamen-tally limited by the horizon limits of the
observable universe.
LC
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