Has Koelman Successfully Eliminated Dark Energy Thanks to the Recent Work of Verlinde?

"Hammock Physicist" Johannes Koelman has made a bold statement at his blog regarding the title of this blarticle, which I strongly recommend we read then examine by clicking here. Read the replies as well, as they're also interesting and no less important.

Essentially, the bulk of Koelman's work is as follows, and in his words from his article:

I previously posed the question “can dark energy, just like gravity, be understood as an entropic effect?”.

To my astonishment, it appears that a quick 10 minute exercise in determining the entropic force exerted on the entire observable universe indeed yields an effect with the right order of magnitude to explain the cosmic dark energy (or cosmic acceleration). It seems that a dark energy effect emerges from Verlinde's holographic description. All 123 orders of magnitude of the dark energy mismatch evaporate when considering the cosmic acceleration as a result of a holographic entropic force.

The line of reasoning is as follows (for ease of notation I will work in natural units and leave out factors c, G and h-bar):

1. Consider the cosmic horizon (the edge of the observable universe: a sphere with radius R approximately equal to 2.7 10^61 in natural units)

2. According to the holographic principle the observable universe is encoded in N = pi R^2 bits located at the cosmic horizon,

3. A finite temperature T is associated with this horizon. This temperature is determined by an equipartition of the energy Mc^2 contained within the horizon over the bits (degrees of freedom) associated with the horizon. Here M = 1.4 10^60 is the observable mass of the universe. Using the equipartition expression ½kT = M/piR^2, it follows that kT = 3 10^-64.

4. An entropic force F = kT grad(N) = kT grad(pi R^2) =2 pi kT R is associated with the horizon. This results in a cosmic expansion (1/R) d^2 R/dt^2 = F/MR = 2 pi kT / M = 1.3 10^-123. Presto!

--- Postscript ---

Two critical notes to the above speculative derivation need to be mentioned here:

1. As I set out to explain more than a hundred orders of magnitude mismatch, I have not bothered myself with numerical factors of order unity. As a result,the end result could be off by a factor of two or so.

2. More importantly, a full evaluation of the above simple expansion model yields an expansion (1/R)d^2R/dt^2 = (2c/R)^2. Whilst this expression yields the right order of magnitude for the expansion, it is not constant and therefore not in line with the full Lambda-CDM model cosmological model. Is it a coincidence that the current value of the dark energy density comes out right? Or does the Lambda-CDM model need a modification?

Erik Verlinde (b. 1962)