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Re: [Phys-l] DARK ENERGY



In a message dated 5/7/2007 3:51:38 P.M. Eastern Daylight Time,
Faraday321@aol.com writes:

A topic of considerable discussion on this list, at least in the past was
dark energy. I would like to offer another twist on this suggested by a
recent
paper by Afsar Abbas on this topic.

)))))))))))))))))))))))))))))))))))))




This was posted on another list which explains this comment.

Bob Zannelli

))))))))))))))))))))


The classic Marble and wood equation from General Relativity is well known


G_mu,nu= kappa* T_mu,nu



However this equation makes a static Universe impossible so Einstein
added his famous fudge factor, the Cosmological constant.

G_mu,nu + Lambda*g_mu,nu = kappa*T_mu,nu


Since this is a classical theory Lambda can be thought of as a
curvature term. The story is well known. The discovery that the Universe
is not
static after all caused Einstein to remarks that the inclusion of this term
in
his equation was his biggest blunder.

However, be this the case or not, there is no reason to set Lambda to
zero. Many years later Weinberg demonstrated that the Zero point energy of
the
quantum fields was equivalent to Einstein's cosmological constant. What was
worst, QFT predicted an immense value which would have blown the Universe
apart
long ago. I think it's fair to say that the general view in the physics
community was that some new symmetry was needed to set the vacuum energy to
zero. We have,


H= w*(a^dag*a+1/2)


Causing the Einstein equation to be written as


G_mu,nu + Lambda*g_mu,nu = kappa*T_mu,nu - kappa*rho_v


Where rho_v is the vacuum energy created by the quantum fields.



However, most often the geometric terms is set to zero so we can write the
equation as

G_mu,nu = kappa*T_mu,nu - kappa*rho_v


One such symmetry proposed to cancel out the ZP energy were the negative
energy states normally discarded as being unphysical. ( Pauli) This idea in
various forms has become somewhat popular having been proposed by Klauber ,
Moffat, Sumdrum and Kaplan, T Hooft and Nobbenhuis, Quiros, Hans-Thomas,
Elze,
Andrianov, Cannata,Giacconi, Kamenshchik, Soldati, Linde and others.

While this proposal takes various forms, in terms of the operator
formalism
,. it is proposed there is a hidden sector with a negative Hamiltonian


a_n= -i*a^dag a_n^dag= -i*a


H_n =-H = - w*a_n^dag*a+1/2)

So that we would expect to get

G_mu,nu = kappa*T_mu,nu - kappa*rho_v +
kappa*rho_vn = kappa*T_mu,nu


However, based on data gathered from the SN1A super Nova
survey, as well as WMAP data , there is good reason to think that in fact
we
need to include a CC term in Einstein's equation in some form after all.

The physicists who had proposed using the negative energy states to solve
this problem looked to an imperfect cancellation of positive and negative
energy states to explain the observed CC. This included Linde, Klauber,
Moffat,
Sumdrum and Randel , Andrianov, Cannata,Giacconi, Kamenshchik, Soldati,
Linde and others. However, none of these models seemed very natural or
workable.


However perhaps going back to the original spirit of Einstein's
inclusion of the CC term might be a way forward. This is no known reason
why the
geometric CC should be set to zero. Unlike the quantum field contributions
there
seems to be no symmetry to drive this term to zero. So it seems possible
that the mysterious dark energy is a result of the geometry of space time.

However, just as a vacuum energy must result in a curvature term in
Einstein's equation , a curvature term must result in a vacuum energy. In
fact we
can view the curvature term and the resulting vacuum energy as two
different
ways of describing the same thing. So given the equation


G_mu,nu + Lambda*g_mu,nu = kappa*T_mu,nu -
kappa*rho_v + kappa*rho_vn


We get after complete cancellation of the ZP energy.

G_mu,nu + Lambda*g_mu,nu = kappa*T_mu,nu


Now if we did an inventory of the Universe we get


BARYONIC MATTER

mass = 1E6 to 1E7 ev

number of quanta = 1E78

Percentage of Universe = 5 percent


RADIATION

mass = 1E-4 ev

Number of Quanta = 1E27

Percentage of Universe = .005 percent.



HOT DARK MATTER

mass =< 1ev

Number of Quanta = 1E87

Percentage of Universe = .3 Percent


COLD DARK MATTER

mass = 1E11 ev

Number of Quanta = 1E77

Percentage of Universe = 25 Percent

DARK ENERGY

mass = 1E-33 ev

Number of Quanta = 1E118

Percentage of Universe =70 Percent


So the question becomes what are the Dark energy quanta for the
curvature term. Well we are on the unsettled border of GR and QFT. But
fortunately we
can rely on the semi classical formulation which gives us the
Davies-Hawking-Unruh as our source of Dark energy quanta. Based on this
formulation we
should get a Dark Energy particle energy on the order of 1E-33 ev.


We have the Davies_Unruh equation


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


Where a = Lamda*c^2*R/3


Since in a De Sitter space

R=sqrt[3/Lambda]


T= hbar*c*sqrt[Lambda]/( 2*pi) = 5.88 E-53 Joule = 3.68E-34ev


So in summary we can say starting from the ZPE you either get a
ridiculous vacuum energy density ( which of course we don't see) or using
the
negative energy states you get zero vacuum energy density ( which we also
don't
see). But if you start with curvature you can get a vacuum energy density
to
conform to what's observed. Also you get a fundamental arrow of time due to
the decoherence which occurs
via the future horizon created by the geometric CC.

Some perhaps interesting questions assuming this proposal makes sense are
, could this hypothetical geometric structure relate to the mysterious CP
violation ( and associated time reversal invariance violation). What does
this
have to do with inflation? Could there be a fundamental principle which
drives
the overall geometry flat using this "geometric" energy" for inflation?
Is
this curvature time dependent in some way? Does this explain the
coincidence
of the ratio of matter and dark energy ratio?

Of course the really big question is does this make good sense.

Bob Zannelli






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