Cosmological constant replaced by an entropic force?

While I have explained that gravity can't be an entropic force, because of its many fundamental properties such as reversibility and its preservation of the interference patterns, it's still true that there can exist entropic forces in Nature that people have missed.

And some of them may be damn important.

In a thought-provoking hep-th preprint, three very interesting authors, namely Damien Easson, occasional TRF reader Paul Frampton, and recent Nobel prize winner George Smoot try to use an entropic force as the cosmological constant killer - a killer of the pretty woman on the picture:

Entropic Accelerating Universe

Why is the expansion of the Universe accelerating? Somewhat generally, we use the term "dark energy" for whatever entity drives this acceleration. But what is "dark energy"? The conventional story, supported by nontrivial WMAP and other measurements as well as a theoretical realization via a SUSY-breaking de Sitter landscape in string theory, is that there is a small positive cosmological constant in the bulk, around 10^{-123} in Planck units, and a negative pressure numerically equal to it.




Their alternative story is that there exists a previously neglected entropic force trying to stretch the cosmic horizon - to increase its area (and make the bulk more uniform) - because it increases its entropy "A/4", too. The total entropic force, "-dE/dr = -T dS/dr", turns out to be "-1" in the Planck units.



This is how the collaboration leading to this paper began.

If you divide this force by the area "A" of the cosmic horizon, you obtain the pressure. If they did this simple arithmetics correctly, it is equal to

p = F / A = -H²/ (4 pi) = -2/3 rho_critical

in the Planck units. That's not only a realistic value: it seems to explain one non-trivial number, namely why the dark energy contributes about 70% to the energy density in the Universe! We usually say that the right number is slightly above, and not below, 70%, but it's pretty close. (And the current cosmological constant is equal to 66.7% of the critical density at some point in the past - which may give you a hope that if you recalculate the cosmology with this new picture, it may become a full agreement.) I find this prediction or postdiction completely fascinating - a reason to investigate this proposal in detail.

Of course, what I find problematic at this point is the method how one can jump from the "global" quantities describing the Universe to the "local" ones: how can you translate the ordinary differential equations for the "radius of the Universe" to the partial differential equations analogous to general relativity with a cosmological constant. You really need it because the latter is what is observed.

The required homework is not just about finding something new: it's about showing that some calculations in the past had to be wrong because the effective field theory approach missed the entropic force. They suggest it has something to do with the surface terms but I don't understand how surface terms modify the equations of motion in the bulk, away from the horizon.

But who knows, maybe it can be done. And maybe they have an idea how to do so. They talk about "smaller screens" than the cosmic horizon, too. I don't understand the rules of the game here. I think it's not right to associate the entropy with "any" surface in the Universe, and even if one could do it, I don't know how you could derive the right shape of the "surface" in the following moment. The cosmic horizon is defined (and extrapolated) by its causal properties - but the evolution of a "generic holographic screen" (which is really any surface) is not determined by anything.



Dr Smoot, is one million dollars for the Nobel prize enough? Where is Acadia National Park? A) California, yes, B) Maine, no. B) is correct. Hung(a)ry, is it a country? I know Turkey but Hungry...

Of course, because the Universe used to be smaller in the past, their entropically generated cosmological constant was higher in the past, too. It was always 2/3 of the critical density determined by the Hubble constant which would be much higher in the distant past. I don't know what it does with the causal diagram of the Universe.

Let me just mention that this construction doesn't really explain why the observed dark energy is such a small number - around 10^{-123} in the Planck units. It just links it to a large number, the area of the cosmic horizon, 10^{122} Planck areas or so. Of course, these numbers have always been linked - except that the authors try to present the area as the primary one, and the negative pressure (pretending to be the cosmological constant) as the secondary one.

At any rate, after the first glimpse, I find the idea fascinating and not "obviously" wrong. Of course, this may change sooner or later as more data and more accurate analyses and tests arrive or emerge.