[ExI] Question on Vacuum fluctuations and Non-ZeroEnergyEmptySpace:

[scerir]

[the questions by Andres and Bryan
were interesting (at last to me)
so I asked an expert ...]

> Is the vacuum energy density constant
> in the universe?

This depends upon who you talk to --- :-o .
Steinhardt came up with an idea that
the cosmological constant /\ was dependent
(eg no longer constant) upon a field phi,

/\ = /\(phi, phi_{,a}),

and since the cosmological constant is
related to the density and pressure by

/\ = 8pi G/c^2(e + p)

a cosmological term that varies in time
and space means that the energy density e
and pressure p will change as well.
This idea is called quintessence.

Is supect that quintessence is a phase
condition for the universe and vacuum,
along with dark energy and phantom energy.
These have curious analogues to Landau theory
of Fermi fluids in solid state physics.

> Having in mind the universal expansion,
> and if the vacuum energy density is constant,
> does it mean there is a continuous production
> of vacuum energy caused by the universal expansion,
> or causing the universal expansion?

This is one reason for dark energy and
negative pressure.  The equation of state is
p = we, for w a particular number.

The first law of thermodynamics is dE = -dW + TdS.
As you observe if the vacuum density of
the universe is a constant then as the volume
of the universe increases more energy would be
created for free.  Yet the total energy
of the universe should be zero, so we set
dE = 0 and dW = -de, and TdS = dp (units assumed)
we have that
dE = 0 = de + dp,
or in covariant terms
nabla_u(E) = 0 = (e + p)U^a_{;a}
and so we must have e = -p,
or that w = -1.

SN1A and WMAP data put w = -1.02 +- .01 or so.
Now in this first law view what is happening
is that internal energy is being created in
the universe, and so to conserve total energy
the vacuum absorbs work from the universe.

This is why there is negative pressure which we
interpret as dark energy.  This prevents the
expansion of the universe from creating energy
in a runaway process.

> (I can agree these are maybe little stupid
> questions, but I could not find easy answers ...)
> s.

Not stupid, but what is stupid is why nobody
asked these questions before 1997.
Before Perlmutter found SN1A luminosities implied
an accelerated universe it was known that inflation
acted on the universe in much the way I illustrate
above.  I suppose everyone was sure that /\ = 0.
However, once /\ =/= 0 the accelerated universe
and dark energy are almost manditory.  Why nobody
saw this before 10 years ago is almost a mystery.

> " One must be able to say
> 'tables, chairs, beer-mugs'
> each time in place of
> 'points, lines, planes' "
> -David Hilbert
> (returning home to Körnigsberg from
> attending a lecture in Halle, by Hans Wiener,
> on the foundations and structure of geometry).