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[Phys-l] Holographic Dark Energy Crossing into the Phaeton Divide or Not.




Holographic Dark Energy Crossing into the Phaeton Divide or Not.


One possible "explanation" for Dark Energy is known as the Holographic Dark
Energy proposal. Actually like inflation, the Holographic Dark Energy
proposal isn't one coherent theory but rather a family of various models which
making a common generic set of assumptions offer several possible
mechanism to implement the consequences of these assumptions. In this brief post I
will look at a broad brush picture in an effort to flesh out some
observational consequences of idea. Unfortunately as will be shown the broad brush
model offers little hope of finding observational confirmation of this set
of ideas. However, it should be mentioned that several specific models,
especially the Quantum foam Holographic Dark Energy proposal do make potentially
falsifyable predictions that should be testable over the next several
years.

The HDE model is based on the assumption that the available degrees of
freedom in any volume is bound by the surface area measure of that bound. This
relates directly to the Bekinstein Bound, which limit the mass energy for
any given volume as proportional to sqrt[A_sur]/G. This is reflected in the
critical density as defined by the Friedman equation. If the Universe
really underwent a period of sufficient inflation the mass energy should be at
the critical value. We have;

{ (d/a/dt)*(1/a)}^2= H^2=8*pi*G*rho_m/3 - k*c^2/a^2+lamda*c^4/3

Where a is the scale factor, k is the curvature term, rho_m is the mass
energy density, lambda is the cosmological constant and H is the Hubble
parameter.

We can rewrite this in a more useful form since k=0

H^2=8*pi*G/3*{rho_m +rho_vac}

Where rho_vac is the vacuum energy density.


Given the HDE model there are two scenarios for the evolution of the
Dark Energy parameter.

One the Hubble parameter will remain constant. In this scenario as the
scale factor increases the vacuum energy density will increase. In the scenario
the HDE induced vacuum energy crosses into the phantom energy range but no
big rip event will occur as the equation of state parameter will
approach-1 in the predicted big freeze era. Based on the concordance model this
will occur in 1E14 years.

rho(a)=rho(0)*{(a/a_0)^(-1*1+w)}


This gives us an observation value of =1.013.... it is very unlikely our
measurement of the equation of state parameter could ever achieve the
accuracy needed to confirm this value.


The other scenario would be for the vacuum energy to remain constant and
have the Hubble parameter increase. However in this scenario the required
increase in the Hubble parameter is only 3.22E-4% per billion years, again
well out side any possible observational range.

Bob Zannelli













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