Dark energy from logarithmic corrections to cosmological horizon entropy?

mitchell porter

We currently have a thread about logarithmic corrections to the basic black hole entropy formula. I was thinking about attempts to relate the magnitude of dark energy to the area of the cosmological horizon, and about the various analogies made between the cosmological horizon and the horizons of black holes, and I suddenly wondered: could you derive "dark energy" as a quantum correction to the expansion of the universe, directly analogous to the quantum corrections we are discussing in the other thread?

marcus

In very general terms (not at the level of detail where I can't understand it) I like your idea because it is groping in the direction of a Quantum Relativist explanation of Lambda. I suspect that's the right direction to look in rather than QFT. "Vacuum curvature" rather than "vacuum energy".

I should say that for better or worse your idea was prefigured (again only in the most general terms) by a paper I personally didn't feel good about, by George Smoot (the Nob.) and Damien Easson.
Smoot and Easson swooned uncritically into the arms of Entropic Force. It didn't seem Smoot-quality to me. They totally embraced the hot idea of 2008 or whenever. I have to go and get the paper.

Charles Lineweaver, a favorite cosmologist of mine, has a paper calculating the entropy of the cosmic event horizon that might be good to find and consult as a check.

Physics Monkey

Don't we need dark energy as a zeroth order thing to drive the acceleration in the first place? If so, how could it be a quantum correction due to the expansion?

marcus

I had the same reaction at intuitive level. Just a gut feeling that you don't just want it to depend on a correction term. But the general idea of looking for a QG explanation for vacuum curvature seems worthwhile.

Here is the Smoot Easson Frampton paper (alas poor Frampton!)
http://arxiv.org/abs/1002.4278
Entropic Accelerating Universe
Damien A. Easson, Paul H. Frampton, George F. Smoot
(Submitted on 23 Feb 2010 (v1), last revised 24 Oct 2010 (this version, v3))
To accommodate the observed accelerated expansion of the universe, one popular idea is to invoke a driving term in the Friedmann-Lemaitre equation of dark energy which must then comprise 70% of the present cosmological energy density. We propose an alternative interpretation which takes into account the entropy and temperature intrinsic to the horizon of the universe due to the information holographically stored there. Dark energy is thereby obviated and the acceleration is due to an entropic force naturally arising from the information storage on the horizon surface screen. We consider an additional quantitative approach inspired by surface terms in general relativity and show that this leads to the entropic accelerating universe.
14 pages, 1 figure, extended and clarified

marcus

Here is the Egan Lineweaver paper. It contains an estimate of the entropy of the Cosmic Event Horizon (CEH) which can save you the trouble of looking up the radius, calculating the area etc etc. Note that the CEH radius is not the same as the Hubble radius. The Hubble radius is only about 14 billion LY and the CEH is a bit farther. I recommend Lineweaver as a trustworthy source. Also the Smoot et al paper cites this, I see.

http://arxiv.org/abs/0909.3983
A Larger Estimate of the Entropy of the Universe
Chas A. Egan, Charles H. Lineweaver
(Submitted on 22 Sep 2009 (v1), last revised 25 Jan 2010 (this version, v3))
Using recent measurements of the supermassive black hole (SMBH) mass function, we find that SMBHs are the largest contributor to the entropy of the observable universe, contributing at least an order of magnitude more entropy than previously estimated. The total entropy of the observable universe is correspondingly higher, and is S_obs = 3.1[+3.0-1.7]x10¹⁰⁴ k. We calculate the entropy of the current cosmic event horizon to be S_CEH = 2.6[+-0.3]x10¹²² k, dwarfing the entropy of its interior, S_CEHint = 1.2[+1.1-0.7]x10¹⁰³ k. We make the first tentative estimate of the entropy of weakly interacting massive particle dark matter within the observable universe, S_dm = 10⁸⁷-10⁸⁹ k. We highlight several caveats pertaining to these estimates and make recommendations for future work.
ApJ. Accepted 11 Jan 2010. 10 pages and 10 figures. Colour version

MTd2

Isn't it more likely to be responsible for dark matter than for dark energy?

If you think in terms of potential slopes and holography, it wouldn't matter much since it would represent only a small correction to the area of the apparent horizon as seen from each point, FRW cosmology (thinking about Bousso here). But thinking about ordinary mass, it would give a mond like linear correction to gravitational potential. More, it would give viscosity to gravity, making it appear to apparently decouple from ordinary matter, as we usually see in galaxy collisions.

Helios

Does entropic gravity theory, which considers dark energy to be the entropic force exerted by the cosmological horizon, win a blue ribbon for the best explanation of the dark energy enigma? I've heard other explanations which end up hypostatizing some strange exotic form of yet-to-be-discovered matter. There are surely many other explanations as well. Is there more enthusiasm for a different explanation of the dark energy enigma than entropic gravity theory?

marcus

There certainly is on my part! The simplest explanation of the observed acceleration is that the GR equation naturally contains a curvature constant Lambda. It's a constant like Newton's G constant. If you think we need an explanation about why Newton G is the size it is, then of course we need an explanation for the vacuum curvature constant about that much.
More about that in this post:
http://physicsforums.com/showthread....97#post3803497

That thread has a link to a paper "Why all these prejudices against a constant?"
As explained in the paper (and in a companion piece in Nature magazine) there is no reason to mis-identify Lambda as an ENERGY and make up stories about exotic particles. You CAN do that but it's apt to make life more complicated---great "mysteries". The biggest puzzle ever faced by Science and all that ...

Since it is a curvature constant, the unit of Lambda is reciprocal area. Because it is small, it is the inverse of a large area. My attitude is it is simply one over a certain area which is a constant of nature. Someday we probably will discover explanations for one or more natural constants---maybe there is an underlying reason why Planck's hbar is the size it is, G the size it is, the speed of light, Lambda, or the area it is the reciprocal of, or the length constant which is the square root of that area---a natural length scale that may have other roles it plays in nature. But for now it's just a fundamental constant of nature. IMO.

apeiron

This always seemed like a natural approach to dark energy to me. It fits a top-down view where the universe is being driven to flatness, and you are left with a Planck-scale "creep" of metric expansion due to uncertainty.

It seems to be what Paul Davies - who works closely with Lineweaver - is speculating here....

marcus

Hi Apeiron! Intriguing speculation by Davies.

Hi Mitchell, I don't want to get away from your original idea. I think I misunderstood, and didn't catch your drift when I made the connection to Entropic Force and the Smoot Easson Frampton paper.
It chimes with what you said about "attempts to relate the magnitude of dark energy to the area of the cosmological horizon" but it doesn't bear directly on what I now see as your main focus---wondering if you could derive acceleration as a "quantum correction to the expansion of the universe".

So as to avoid distracting the thread I want to abandon CEH entropy for the moment and try for something hopefully closer to your idea of a quantum correction in the geometric evolution of the cosmos. Maybe you could restate what you are speculating about at greater length and let me take another shot at relating it to what I remember of the relevant literature.

I recall there was a 2002 paper by Martin Bojowald where he explored the idea that Lambda could arise as a quantum correction. It was from ten years back--but you may have seen it.
It was frankly speculative and may never have gone anywhere. Could the general idea be revived after 10 years of comparative neglect?
http://arxiv.org/abs/gr-qc/0206054
Inflation from Quantum Geometry
Martin Bojowald
(Submitted on 18 Jun 2002)
Quantum geometry predicts that a universe evolves through an inflationary phase at small volume before exiting gracefully into a standard Friedmann phase. This does not require the introduction of additional matter fields with ad hoc potentials; rather, it occurs because of a quantum gravity modification of the kinetic part of ordinary matter Hamiltonians. An application of the same mechanism can explain why the present-day cosmological acceleration is so tiny.
4 pages, 3 figures

Bojowald refered briefly to the earlier paper on page 14 of this 2007 article http://arxiv.org/abs/0705.4398

3.3 Effective negative pressure
Rather than understanding dark energy as the vacuum energy of quantum fields, it could be a quantum effect which, when expressed in a Friedmann–Robertson–Walker solution, resembles an effective matter contribution giving rise to negative pressure. In loop quantum gravity, an explanation of dark energy could be provided in this manner. In isotropic models, loop quantum cosmology has revealed a source for negative pressure from quantum corrections (Bojowald, 2002a). This happens on small scales where quantum geometry modifies the behavior of functions such as the inverse volume which classically diverge at zero spatial extension. As seen in Fig. 2, the isotropic quantum version of the inverse cuts off the divergence and bends the curve down to zero (Bojowald, 2001b).5 Effective matter Hamiltonians, which always contain the inverse determinant of the densitized triad, are thus increasing as functions of volume at early times which replaces the classical decreasing behavior. It is then easy to see why negative pressure arises: by thermodynamics pressure is defined as the negative derivative of energy by volume. If energy starts to increase with volume when small scales are reached, negative pressure automatically results.

In 2005 or 2006, Ashtekar and a bunch of other people revised Bojowald's initial formulation of Loop cosmology. So at the detail level the picture has changed a great deal since 2002!
I would guess that the effect that Bojowald conjectured back in 2002 has not been sustained. However it might be worth noting anyway, just in case something interesting has been missed. It seems also to accord with what you were wondering about.