Subj: Re: Holographic dark energy models: A comparison from the latest
observationa... Date: 6/12/2009 2:55:19 PM Eastern Daylight Time From:
RBZannelli@AOL.COM Reply-to: AVOID-L@HAWAII.EDU To: AVOID-L@HAWAII.EDU
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In a message dated 6/12/2009 1:39:15 PM Eastern Daylight Time,
RBZannelli@AOL.COM writes:
Holographic dark energy models: A comparison from the latest observational
data
Authors: Miao Li, Xiao-Dong Li, Shuang Wang, Xin Zhang
Comments: 13 pages, 4 figures
Subjects: Cosmology and Extragalactic Astrophysics (astro-ph.CO); General
Relativity and Quantum Cosmology (gr-qc)
The holographic principle of quantum gravity theory has been applied to the
dark energy (DE) problem, and so far three holographic DE models have been
proposed: the original holographic dark energy (HDE) model, the agegraphic
dark energy (ADE) model, and the holographic Ricci dark energy (RDE)
model. In this work, we perform the best-fit analysis on these three models, by
using the latest observational data including the Union+CFA3 sample of 397
Type Ia supernovae (SNIa), the shift parameter of the cosmic microwave
background (CMB) given by the five-year Wilkinson Microwave Anisotropy Probe
(WMAP5) observations, and the baryon acoustic oscillation (BAO) measurement
from the Sloan Digital Sky Survey (SDSS). The analysis shows that for HDE,
$\chi_{min}^{2}=465.912$; for RDE, $\chi_{min}^{2}=483.130$; for ADE,
$\chi_{min}^{2}=481.694$. Among these models, HDE model can give the smallest
$\chi^2_{min}$. Besides, we also use the Bayesian evidence (BE) as a model
selection criterion to make a comparison. It is found that for HDE, ADE, and
RDE, $\Delta \ln \mathrm{BE}= -0.86$, -5.17, and -8.14, respectively. So, it
seems that the HDE model is more favored by the observational data. http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.0928v1.pdf
It might be noted that my most recent post on Dark Energy was a version of
RDE. That is proposing that holographic boundary given by horizon related
to the average radius of the Ricci scalar Curvature. ( See full post below)
This is a version of Induced HDE. It should be noted that any simple
dynamic HDE model produced an equation of state that precludes accelerated
expansion. This can be easily seen.
Rho(a) = a^-3*(1+w)
1/a^2= a^-3*(1+w)
-2*lna = -3*(1+w)*lna
w= - 1/3
Therefore the HDE model precludes any horizon which scales with the scale
factor.
Where alpha is a numerical constant. Per my proposal where
rho= 2*H^2Ghbar/c^5*Integral Dw L and dH/dt=0
alpha = {16*piG^2*hbar/c^5}*Integral Dw L
See Below.
INDUCED GRAVITY AND HDE
Several earlier posts explored the idea that of the Holographic dark
energy proposals modeled in terms of some form of induced gravity model.
In this
post I would like to flesh out this idea in a little more detail. The
basic
idea in induced gravity is that gravity is in fact not a fundamental force
but rather an induced effect of the collective action of all the Quantum
fields. Specifically that a gravity field is really a modification of the
action density of the vacuum states in the vicinity of collections of
matter
energy. As Sakharov writes "Vacuum Quantum Fluctuations in Curved Space
and
the Theory of Gravitation"
"Considering the density of the vacuum Lagrange function in a "
simplified" model of the theory of non interacting free fields with
particles m=aprox
k_0 shows that fixed ratios of the masses of real particles and "ghost"
particles (i.e., hypothetical particles which give an opposite
contribution
to that of the real particles to the R dependent action)."
In notion previously introduced we might write then;
T_nu,mu = g_mu,nu* { Chi(-) Intergral Dw L(+) + Chi (+) Integral Dw L( -)
}
Here we can define the factoring functions chi+-) as
chi(+-) = 1/gamma_g (+-)^2
gamma_g (+ -) =1/sqrt [ 1 +- 2*G*M/R*c^2]
Based on this approach given the Einstein equation
Where rho_global*g_mu,nu represents the dark energy contribution to the
Einstein Tensor.
So how might we write the factoring function for the global vacuum energy
contribution? It would seem this function must be in terms of the Hubble
parameter. So we might propose
chi ( +- )= 1/gamma(+-)^2
gamma( +-)= 1/sqrt [ 1 +- a_lambda^2/ a_planck^2]
Where a_lambda is the acceleration due to dark energy and a_plk is the
Planck scale acceleration