Holographic Universe and Dark Energy

On Jan 5, 2005, at 4:28 PM, Carlos Perelman wrote:

Dear Christian (Jack and Tony):

In the paper by Zee and Hsu : hep-th/0406142

they discuss the issue of the time dependence of the infrared scale and Cohen, Kaplan and Nelson paper in Phys. Rev. Letts (1999), but these authors do not derive the geometric mean relationship.

Note that In de Sitter or Anti de Sitter space, as I have shown, you set the infrared scale to be given by the *throat* size of the hyperboloid (that describes de Sitter, Anti de Sitter space), which is a *constant* parameter.

OK good. It must be "constant" because w = -1 demands it.

Energy Density ~ R(t)^-3(1 + w)

OK what I am saying is that

"throat size" = Lp/(1 - Lp^n|Vacuum Coherence|^2)^1/2 ~ 10^28 cm

Einstein Cosmological Constant /\ = (throat size)^-2

n = 2 in World Hologram picture - that George Chapline Jr rejects BTW.

n = 3 in usual space picture

Normalize macro-quantum Vacuum Coherence ODLRO parameter to 1/(Length)^n/2 like micro-quantum waves in n space dimensions.

The people who advocate Holography say that you equate the infrared scale with the size of the future event horizon of de Sitter space = an asymptotic unreachable scale.

Of course, we know that the Hubble radius is time dependent. Thus to be precise, we must use the geometric mean relationship using an ulraviolet Planck scale and an asymptotic infrared (constant) scale (throat size of hyperboloid).

The point is that you cannot have any dependence of Einstein's cosmological constant /\ on the scale factor R(t) or on H(t) = R(t)^-1dR(t)/dt.

Note, the quantum gravity world hologram uncertainty formula

(Uncertainty in measurement of length l)^2 = &l^2 > hl/mc Wigner quantum clock of mass m

&l > Gm/c^2 to avoid forming a quantum black hole

multiply

&l^3 > lhG/c^3 = lLp^2

Uncertainty in measurement of throat size is then

&l > [(throat size)(Planck area)]^1/3

If throat size ~ c/H ~ 10^28 cm

&l > (10^28x10^-66)^1/3 = 10^38/3 ~ 10^-13 cm ~ 1 fermi, i.e. 1Gev scale of universal Regge slope of hadronic resonances that are in some ways like rotating black holes in strong short-range gravity as I published in "Collective Phenomena" edited by Herbert Frohlich & F.W. Cummings, 1973.

hardly a random coincidence.


In my paper I have an underlying 5-dimensional Topological theory, and as Dirac pointed out long ago, when you have higher dimensions, one cannot exclude the possibility of a time variation of the four-dimensional fundamental constants in Nature, like the Planck scale (Newton's constant) resulting from compactifications of the extra dimensions.

The problem is w = -1 is a strong constraint from covariance and the principle of equivalence. That hit me in the I lika bigga piece of Pi in The Sky only today! :-)

Best wishes

Carlos



On Jan 5, 2005, at 1:40 PM, Jack Sarfatti wrote:

1. The entropy of universe from World Hologram as

S(Universe)/kB ~ R(t)^2

has nice feature that it solves Roger Penrose's problem with inflation of why early universe has low entropy, i.e. why Arrow of Time is in direction of accelerated expansion of space since

R(initial singularity) ~ 0 << R(today) ~ 10^61

However, George Chapline Jr objects to the whole Bekenstein-Hawking entropy ~ surface idea that is the basis of the t'Hooft-Susskind hologram. I sit on the fence on that for the moment.

However, I retract my hologram model where

/\ = (LpR(t))^-2

because it violates w = -1 for zero point energy.

That is the energy density of any "stuff" both real and virtual obeys

energy density ~ R(t)^-3(1 + w)

w = 0 for v/c << 1 real matter

w = +1/3 for radiation (real photons)

w = -1 for RANDOM INCOHERENT virtual quanta of all kinds

The energy density for ordinary matter ~ 1/R(t)^3 and ~ 1/R(t)^4 for radiation. But the dark energy density must be truly constant i.e. independent of R(t).

In my theory, Einstein's Cosmological Constant is

/\ = Lp^-2(1 - Lp^n|Vacuum Coherence|^2) ~ 10^-56 cm^-2

n is either 2 or 3 depending if you believe t'Hooft-Susskind hologram or not.

The formula must be more like what Carlos Perelman is saying

/\ = (H/c)^2

Where H is some truly constant asymptotic value of H = R(t)^-1dR(t)/dt

So that the future of our Universe is quasi-inflationary

R(t) ~ e^Ht

In that case.

OR alternatively we do not use H, but introduce another contingent CONSTANT parameter /\ in the sense of the WEP and the infinity of parallel material IT worlds as explained by Max Tegmark on his website.


On Jan 5, 2005, at 4:05 AM, Carlos Perelman wrote:

Dear Christian, Brian, Jack and Tony :

I recall that Christian ( Beck ) wrote a very nice paper about vacuum fluctuations related also to
Brian's ( Josephson ) work. In any case, let me tell Christian ( since he does not know ) about the origins of the Geometric mean relationship among the vacuum energy density
involving the upper and lower scales that is also related to the *neutrino* mass :

rho = ( L_Planck )^{ -2 } ( R_Hubble )^{ -2 } =

Oh OK you mean in my notation, using truly constant throat size

Dark Energy Density = hc/Lp^2(throat size)^2

Where in my Vacuum Condensate theory

1/(throat size)^2 = (1/Lp^2)(1 - Lp^n|Vacuum Coherence|^2) ~ 10^-56 cm^-2


( L_Planck )^{ -4 } ( L_Planck / R_Hubble )^{ 2 } ~

10^{ - 122 } (M_Planck )^4 = ( neutrino mass )^4 = agrees with Observations !

The neutrino mass you get from the above relationship is about 10^{- 3} electron volts = okay

Christian can see the *derivation* from first principles of
such geometric mean relationship described above in my paper :

Mod. Phys A vol 17 , No. 32 ( 2002 ) 2095-2103.

Anti de Sitter Gravity from ( topological ) BF-Chern-Simons-Higgs Theories

In page 2098 I provide the derivation of such geometric mean relation from scratch.

The throat size of Anti de Sitter also coincides with the throat size of de Sitter space and one can take the future horizon scale of the FRW metric ( Jack's model ) to coincide with the de Sitter throat size.

Anyway, I will not bore you anymore with these messages. It is very curious these results.

Happy New year

Carlos Castro Perelman