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[Phys-l] Holographic Dark Energy from Spacetime Foam.




Holographic Dark Energy from Spacetime Foam.
Some physicists support the assertion that spacetime is a kind of Quantum
foam resulting from Quantum fluctuations of the vacuum Gravity field. Accepting
this assertion provides a new road to a model of Holographic Dark Energy. A
Newtonian Analysis of the energy condition of the Universe in accordance with
the FRW equations is helpful with regard to this approach. To be sure the
whole notion of global energy conservation is problematic in the General
Relativity formalism given a non constant scale factor. Energy conservation is the
conserved parameter associated with time translation invariance which seems
undefined given an expanding space time. Therefore any attempt to deal with
global energy conservation in the Universe must rely on Heuristic arguments.
Based on the FRW equations;
rho_crit(mass)= 3*H^2/(8*pi*G)
Where H is the Hubble parameter.
M_crit= rho_crit(mass)*V_h
Where V_h is the Hubble volume. Given that;
R_h= c/H we get;
M_crit=c^3/(2*H*G)
We can calculate the total mass related energy of the Universe by summing
over all masses.
Therefore in any given frame;
E_mass= SUM {all i} gamma_i*m_i*c^2
Where gamma_i is the lorentz transform associated with each mass.
We must also include the Negative gravitational energy which is given by'
E_g = - SUM {all i} m_i *gamma_i*omega*M_crit/ R_i
Where Omega is the density parameter.
Given the homogenous nature of the Universe at large scale we can define R_i
as the average distance between gravity masses.
R_i=R_ave=R_h/2= c/(2*H)
Therefore
E_g= SUM {all i} gamma_i*m_i *Omega*c^2
This gives us
E_unv =E_mass - E_g
E_unv = [ 1 –Omega]* SUM {all i} gamma_i*m_i*c^2*
We can see that ;
Omega >1 E_unv <0 K = 1
Omega< 1 E_unv >0 K=-1
Omega =1 E_unv =0 K=0
Where K is the curvature parameter.
Therefore based on this Inflation creates a zero energy Universe. Note
however, that values of Omega <> 0 also do not violate energy conservation in the
BIVERSE model, though it's difficult to see how such Universes could result
from Inflation.
Based on this we can assume that it is a fundamental principle of
inflationary theory that Universes will have an Omega parameter equal to 1 as seems to
be the case for our Universe based on the preponderance of the evidence.
In accordance with the Holographic principle (HP) the Quantum fluctuations
of spacetime are given by;
delta[L] = > L^1/3*L_plk^2/3
Where L is the scale under measurement and L_plk is the Planck length.
L_plk= sqrt[hbar*G/c^3]
If we map a volume of spacetime L and a temporal extent L/c. (hereafter we
put all multplicative constants at unity to simply the argument) the total
mass (M) must be less than 1/G which corresponds to an energy density of;
rho =< 1/(L*L_plk)^2
It follows that the number of possible elements , again based on the HP is
given by
N=L^2/L_plk^2.
This elements (cells) represent a volume bounding a surface area.
V= Integral dx A
We know that the sum of dark and Baryonic mass falls short of the predicted
energy density by about 73 percent. However, the energy condition established
by inflation requires a critical energy density. Therefore we might assert
that the vacuum energy density is required to be at a value to bring the total
energy density to the critical value. Therefore ;
rho_crit= (H/L_plk)^2= approx 1/(R_h*L_plk)^2
And based on the HP
S= H*R_h^3/L_plk^2
Since
dE/dS=T = E_ave/k
Where k is Boltzmann's constant
We have;
E_ave = approx pho*R_h^3/ S = 1E-31 ev.
Pressure related to a Quantum field is given by the Kinetic energy term
minus the potential energy (absolute value) And since long wavelength quanta
carry negligible kinetic energy this effective scalar field potential can provide
the source of negative pressure that is driving the acceleration of the
cosmic expansion.
An equivalent way of describing this is to assert that the future horizon
creates a measurement process of the virtual vacuum Quantum states. In effect
this model is a special case of the K Essence scalar field model based on the
general class of Induced Gravity models.
Bob Zannelli

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