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 UniverseWhy 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 = -Hin 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.^{2}/ (4 pi) = -2/3 rho_{critical}

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.

## snail feedback (7) :

Hi, I hope you don't mind a possibly unenlightened question from an amateur.

In the early days of dark energy, they said the velocity of expansion was increasing now because accelerating effects of dark energy were proportional to volume, and the volume of the universe had become sufficient to produce an acceleration that more than offset the decelerating effects of gravity. As I recall they added that it was too soon to know if the number you multiplied the volume by was constant over time, or might have changed over the course of billions of years.

Then, a couple of years ago, I remember reading that extensive measurements of that number, taken at various distances away, and thus at different times in the history of the universe, showed it to be constant, to a high degree of precision. Thus the increasing frequency of references to dark energy as the cosmological constant, and fewer references to ideas for dark energy that changed its strength over time.

Therefore, I'm puzzled by your statement that this new theory would produce an "entropically-generated cosmological constant" that changed radically since the early days of the universe when the Hubble constant was much higher. Isn't there an inconsistency here, or do I have my facts or concepts wrong (a strong possibility!)?

"...that pretty woman on the picture."

Lately a few times in my neighborhood I've seen a woman with almost exactly that face. Well, minus the blue eyeshadow. The picture's swirls happen too when she walks. With her evident power over spacetime geometry and her entropic force (making my brain decay to an irregular verb), I have to agree that Smoot and company may be on the right track.

Smoot's idea is essentially the same as Sarfatti's e.g. references on http://stardrive.org Sarfatti also computes the acceleration from the Unruh effect at the de Sitter horizon. However, he points out that the horizon is in our future not our past.

brodix(not Anita)

What gets me about the cosmological constant is that Einstein added it to balance gravity and keep space from collapsing to a point. Given that Omega=1, thus the expansion and gravity are inversely proportional, it would seem that space is expanding between gravity wells at the same rate it is falling into them.

If space is entering stage left at the same rate it is existing stage right, it would seem the stage is always the same size. So why is it assumed the universe is expanding?

Yes, light from the most distant galaxies is redshifted proportional to distance, but what if the light we see is entangled with that falling into gravity wells and so we only see the light that's "squeezed out," but not that being "squeezed in" to gravity wells?

Recently light was detected from very distant sources, which were described as young galaxies, because their light only came from the lightest and bluest end of the spectrum, but wouldn't any red light they emitted have fallen off the visible spectrum and only be more black body radiation?

Suffice to say, I'm not totally sold on the Big Bang theory. Entropy only applies to a closed system, but if the universe is infinite, then our area would be absorbing energy at the same rate it is emitting it. Otherwise Big Bang theory still has to explain from where the energy of the singularity came.

Dear brodix,

if you want to explain the redshift of distant galaxies by some local disturbances or wells or local explosions etc., you will end up with equally complicated or sophisticated descriptions of the Universe as the Big Bang that are moreover less symmetric because they need to imply the unlikely assumption that we're at the "center" of the Universe - because all other points would see some huge anisotropy in your picture.

That's very unreasonable and makes the theory unlikely, given the fact that we haven't seen any "qualitative" anisotropy of this magnitude.

Also, you're wrong that the Big Bang cosmology creates energy out of nothing during the Big Bang itself. It's just not true. In general relativity, the energy conservation law doesn't hold in this simple sense.

For example, the total energy stored in the cosmological constant is exponentially increasing when the cosmological constant exponentially inflates the volume of space - simply because the energy density is constant, by definition.

Also, the energy of a photon or another particle of radiation goes like 1/R (so it is also not conserved) where R is the current "radius" of the Universe - simply because its wavelength is growing with the size of the Universe, too. And the wavelength is inversely proportional to the energy of a photon. (An idea to imagine: the number of waves that can be squeezed along an "equator" of the Universe has to be unchanged.)

So the total energy of the Universe during the Big Bang may be close to zero, and it probably was. Moreover, in the Euclidean space - an analytical continuation of the Minkowski Universe - the beginning of the Universe may be completely smooth. Check papers about the Hartle-Hawking wave function etc.

So I have gone through your text and I am absolutely certain that you haven't offered any rational evidence against the Big Bang Theory whatsoever.

Best wishes

Lubos

Lubos,

No, i'm not saying we would be at the center of the universe, because it would amount to an optical effect, due to the fact that we can only measure the light which has crossed the greatest distances, not all that which has collapsed into gravity well and otherwise grounded out on mass obstacles.

Originally Big Bang theory assumed it was an expansion of the universe in space, but because of the apparent effect that we appear at the center, it was changed to an expansion of space. Now, if space is expanding, wouldn't our most basic measure of it, lightspeed, necessarily have to increase as well? The problem with that is that even if two objects are a billion lightyears apart, should the universe double in size, they would still be a billion lightyears apart, because the speed of light would increase proportionally. Otherwise, if they are now two billion lightyears apart, that is simply an increasing amount of space, not expanding space. Then you get back to the problem of why we appear at the center. How is it that we can say space is expanding, but still have a stable lightspeed to measure it against?

We understand that gravity bending light is an optical effect, in that it doesn't actually move the source of the light, only bends its path. Are we really sure that because there is an opposite effect, the Cosmological Constant, that it is actually moving the sources and not just a way to stretch the lightwaves that manage to travel the furtherest distances?

brodix

Dear brodix,

let me assure you that if 1) you don't make the Universe spatially uniform, like in the Big Bang cosmology, and 2) if you don't put the Solar System to the middle of the Universe, you will observe different patterns in different directions, something that we definitely don't observe (outside our galaxy). So the combination of these two assumptions is pretty much ruled out.

The speed of light is a dimensionful quantity, so whether it's constant depends on the choice of units. But in all existing units used today, which are pegged to meters and seconds, the speed of light is constant by definition because one meter is defined as the path traveled by light in 1/299,792,458 of a second. As you may see, it follows that the speed of light is 299,792,458 m/s, and it has always been. Adult theoretical physicists use units in which c=1 to simplify the matters.

The second itself (and indirectly, the meter too) is defined as a multiple of some period of electromagnetic radiation emitted by a particular type of atoms. It's pegged to the microscopic objects and doesn't care about the expansion of the Universe.

There is an objective fact about the expansion: the ratio of the visible Universe divided e.g. by the size of the atom is growing. You can't handwave this away, or obscure this simple fact by incomprehensible diatribes about the choice of units because the expansion of the Universe doesn't depend on the units.

You: How is it that we can say space is expanding, but still have a stable lightspeed to measure it against?

Sorry, I really don't understand your problem. It's like asking How can Venus be a planet if 2+2=4 at the same moment? Well, yes, both of these things are true. They don't contradict one another in any way. The speed of light is one quantity and the size of the Universe is a completely different quantity, with different units, referring to a different (and more specific) object.

You: We understand that gravity bending light is an optical effect, in that it doesn't actually move the source of the light, only bends its path. Are we really sure that because there is an opposite effect, the Cosmological Constant, that it is actually moving the sources and not just a way to stretch the lightwaves that manage to travel the furtherest distances?

Holy crap, what to do with such long sequences of nonsense? First of all, the cosmological constant is not the "opposite effect" to gravitational lensing. Gravitational lensing is an effect of gravity on light that depends on the particular situation, gravity sources, and direction of the light. The cosmological constant is a term in Einstein's equations that makes the space expand everywhere uniformly.

Second, it's easy to distinguish whether a distance between two objects is "really" increasing or it is just an optical illusion. Just measure the distance in some solid way - way that allows you to measure the "size of the atoms" or any other objective quantity that may be used as a unit. Directly or indirectly. At any rate, there doesn't exist any difficulty to distinguish real distances from optical illusions of the type you are envisioning.

Best wishes

Lubos

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