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[Phys-l] The Void May Be a De Sitter Space. Some Language Corrections





During the discussion of the nature of the void which was a painfully
philosophic discussion I offered the comment that the solution to the question of
the void may really be a physics question. While what I will relate here has
significant speculative input, I do think it has the advantage of attempting
to look at this from relatively familiar physics.

The discovery in 1998 that the expansion rate of the Universe is
accelerating certainly must be the second most important astronomical discovery of the
20th century. This data on this is now pretty conclusive. In addition, though
far from certain, the mechanism for this acceleration appears to be
Einstein's infamous cosmological constant. If in fact this is true, than we can make
some reasonable assumptions about the future of our Universe. Most
interestingly this may mean that our Universe is the mother of future Universes, as
perhaps all Universes are. We shall see this creates a fractal like history in
the multiverse.

If the acceleration of our Universe is due to the cosmological constant
than the future state of our Universe is an empty De Sitter space. Based on
proposals by J Garriga and Alex Vilenkin a De Sitter space with a positive
vacuum energy is not perfectly stable. The basic idea is very simple. Unlike an
empty Minkowski space a De Sitter space has a non zero temperature. It is east
to see why.

Given

T=[ hbar/(2*pi*c*K)]*a

Where K is Boltzmann's constant and a is acceleration

We can that in a De Sitter space this becomes

T= hbar*Lambda*c*R/(2*pi*K)

Where Lamda =[ 8*pi*G/c^4]*<rh0_vac>

Given that

R=1/sqrt[lambda]

We that

T= sqrt[lambda]*(hbar*c/2*pi*K) = H*hbar/(2*pi*K)

Where H is the Hubble constant

Since

H= t/ln[R] = t/ ln [ (1/2*Lamda*c^2*R(0)t^2]


Writing this equation in a time dependent form

T= [ t/ ln [ (1/2*Lamda*c^2*R(0)t^2] *[hbar/(2*pi*K)]


Given this time dependent De Sitter temperature (Gibbons-Hawking
Temperature) we can use the Quantum tunneling probability equation derived by
Carroll and Chen for a Hubble volume



P= exp{ -pi*(m_pl^3/m*T*sqrt[6/m*T]exp[ m/T-3*m/M_pl} /{
pi*sqrt[6/(m*T)]*exp[m/T-3*m/M_pl]}

Where m is the critical mass term for the false vacuum and T is
temperature in energy units.

From this rather nasty equation we can see that at T increases so does
the probability of a Quantum fluctuation into s new Universe somewhere
within the Hubble volume. Of course for any non zero probably a tunneling event is
certain.

From the standpoint of a hypothetical observer outside the fluctuation,
the process of spontaneous inflation presumably looks like the creation of a
small black hole. This means ALL the energy of the fluctuation is "paid back"
to the mother Universe. The creation event is effectively the tunneling of
nothing into a new Universe.

If we make the assumption that new Universes eventually evolves to a De
Sitter Space with a positive vacuum energy than the creation event must
generate inflation in both time directions in a Biverse structure of positive and
negative energy relative to our cosmological arrow of time.


We might also expect that each half of this Biverse would be the CPT image
of the other. The FRW equations governing inflation are inherently time
symmetric and the symmetries of the SM suggest each half of the Biverse is a CPT
image of the other.


R= exp { sqrt[lambda/3]*t}

Assuming Universes has a positive vacuum energy relative to its
cosmological arrow of time than the multiverse has no beginning. It experiences eternal
inflation in both time directions. When represented on a space time diagram
we see a fractal structure for the multiverse history. Therefore time is
endless in both directions. However from a global perspective each Biverse is
can viewed as a timeless Quantum State.

. Finally not each Biverse need have the same vaccua state suggesting the
application of the Anthropic principle. Of course this nice story may not be
true. But it does suggest one answer to the question on the nature of the
void, a question of some contention.



Bob Zannelli




















omnia praeclara tam difficilia quam rara sunt


Ethics (Spinoza)