Dark Energy As An Entropic Force.

(Skip to summary below if you want to cut to the chase and ignore the draining explanation.)


We are going to take time out of our series on the prejudices against dark energy paper and talk about... another paper on dark energy. :)  This is justified because this paper is cool.


Easson, Frampton, and George Smoot (Yes the Nobel Prize winner Smoot who headed the COBE project) recently released an interesting paper showing that one can do a pretty good job explaining dark energy from entropy.


We often assume our universe either doesn't have a boundary, or that if it does its "at infinity" and doesn't really effect us.  These authors took a step back and asked what entropy would do to our universe if it had a consequential boundary.   If it does, we need to add the boundray term we usually ignore to the Lagrangian:

Here R is the term that gives gravity, L is the term that contains the matter of the universe and K is the curvature of our new boundary term.  M is our manifold (space) we live one and the "backwards 6" M means the boundray of the manifold.


Interestingly, if a system has a boundary, the maximal entropy the system can have is directly related to the size of the boundary.  (Thank Steven Hawking for this.)  Because entropy wants to increase, a pressure is exerted on the system to get the boundary to increase.  They calculate the pressure for the given universe and find:

In case you missed it, the pressure exerted on the universe is the same as would be exerted by a cosmological constant making up 2/3 of the total energy of the universe.  Given the cosmological constant is measured at making up ~70% of the universe, this is a remarkable result.


Furthermore, as the boundray increases, so does the pressure.  This causes, not only an expansion of spacetime, but an accelerated expansion!  In fact, the accelerated expansion predicted fits the supernova data (that we use to gauge such an acceleration) remarkably well!  See the plot above.  Hence we read (from the paper above):

Thus, the acceleration of the universe simply arises as a natural consequence of the entropy of the universe, via the holographic principle....  We have discussed a theory underlying the accelerated expansion of the universe based on entropy and entropic force. This approach provides a physical understanding of the acceleration phenomenon which was lacking in the description as dark energy.... The accelerated expansion rate is no longer surprising. It is the inevitable consequence of the holographic information storage on the surface screen of the universe.

If you missed It behind the equations and bad writing:
1.  Assume the universe does have some type of boundary.
2.  Entropy will increase if the boundary can expand. 
3. This induces a pressure trying to cause the universe to expand, incresing the size of the boundary. (And hence entropy.)
4.  The pressure pushing the universe to expand is the same as cosmological constant making up 66% of the energy density of the universe. (It is currently measured at ~70%)
5.  As the universe expands, the pressure actually increases causing an acceleration that matches the cosmic acceleration we observe.


Pretty cool huh? Even if it is not true, at least it is cool.

The 120 Order Of Magnitude Problem.

(The forth post in the dark energy series.)

Now to address the concern the that value of the cosmological constant is off by 120 orders of magnitude from what we expect from theory.  To start off with, let's talk about the Higgs Boson.

The public, media, and many scientists, are greatly anticipating the detection if the Higgs.  Nobody seems to be claiming the Higgs is some mysterious thing scientists seem to know nothing about.  It makes predictions.  It fits the physics well.  It makes the standard model work.  But, like the cosmological constant, it seems experimentally confirmed theory (things like supersymmetry is not confirmed yet.) and experiment disagree by several orders of magnitude about what it's mass should be.

The Hierarchy Problem
This is the famous Hierarchy problem.   Scientists admit to it's existence, but none seem to treat the Higgs as being mysterious. Here's the problem:

1. You calculate the Higgs mass using standard understood QFT.
2. You find that the Higgs mass should be up at the Planck scale because of loop divergences at energy scales we don't understand.
3. From experiment you find that the Higgs mass should be at the 100 GeV scale, (this is several orders of magnitude too small).
4. You invent some unobserved machinery, like supersymmetry, that explains why the Higgs mass should be at the 100 GeV scale after all. (Seriously, string theory and the hierarchy problem are the real reasons why we have supersymmetry.)
5. The media, even the Wikipedia, now nicknames the Higgs as the God Particle and people don't seem to take much issue with it.

Now let's look at the cosmological constant's size.  (Do these divergences make me look fat?)

Back to the paper:

The problem [of the cosmological constant's value] is similar (but worse) to the problem given by the Higgs mass, which scales quadratically in the standard model, and can be taken as an indication that “there is something we have not yet understood” in Higgs physics.

 How similar.  This is how we find the discrepancy:

1. You calculate the value of lambda (the cosmological constant) using standard understood QFT.
2. You find that the lambda should be a "Planck-scale vacuum energy" from loop divergences at energy scales we don't understand.
3. From experiment you find it is very small, about 120 orders of magnitude smaller than this Planck-scale value.
4. You successfully invent some unobserved machinery,  like string theory, that can explain the discrepancy.
5. Everyone maintains the cosmological constant is dark and mysterious.

Maybe it's high energy particle physics that is the real problem.

The problem of the cosmological constant being off by 120 orders of magnitude is analogous to the Higgs' mass being off by several orders of magnitude.   The real problem may have nothing to do with the Higgs or the cosmological constant being weird or mysterious, but may be that we just don't understand physics at high energies.

Now, just to be honest, the machinery needed to fix the cosmological constant problem needs to be more sophisticated than what is needed for the Higgs.

Still, given its analogous nature, in this context, I wonder if the cosmological constant is being treated unfairly.

Coincidence Problems And Dark Energy.

(The third post in the dark energy series.)

One issue that comes up in discussions about the cosmological constant is the coincidence problem.  If dark energy is really caused by a cosmological constant, we seem to be living in a very special place in the universe's history.  Here is an explanation by the the Wikipedia:

The cosmic coincidence problem asks why the cosmic acceleration began when it did. If cosmic acceleration began earlier in the universe, structures such as galaxies would never have had time to form and life, at least as we know it, would never have had a chance to exist. Proponents of the anthropic principle view this as support for their arguments. However, many models of quintessence have a so-called tracker behavior, which solves this problem. In these models, the quintessence field has a density which closely tracks (but is less than) the radiation density until matter-radiation equality, which triggers quintessence to start behaving as dark energy, eventually dominating the universe. This naturally sets the low energy scale of the dark energy.

The point is, many people don't like the idea that dark energy is related to the cosmological constant because if was, it seems like we live in a special place in the universe.  But physicts have been trained to not like theories where we appear to be in a special place.  This causes many to adopt models like quntessesnce where this problem goes away. (Quintessence being the idea that dark energy is related to an oscillating filed, not a constant.)

However, remember, these posts are in favor of the cosmological constant. :)  This is a response. (Beyond the fact that no data supports/suggests quintessence is real. Seriously people!)

Back to the paper:

Say we want to hold a “cosmological principle” stating that we are not in a special place in the universe, in space or in time. Thus, there is a contradiction between the ΛCDM model and such a cosmological principle: to believe that the observed acceleration is caused by a cosmological term in Einstein equations requires us to believe also that we are in a very special moment of the history of the universe. This is the “coincidence argument” against the cosmological constant scenario.

The authors critique this "problem" in a couple of ways.  I am only going to highlight the second:

The cosmological principle cannot be applied uncritically... For instance, a rigorous application of the cosmological principle would lead us to expect that the density around us must be of the same order of magnitude as the average density of the universe (which is manifestly false); or, to put it visually, that the Earth is mostly covered by land and not oceans (most humans observe land and not water around them.)

Humans do not live in a random location on Earth. They leave on land and not on water. Our civilization is not located in a random location in the universe: it is located on a very high peak on the density fluctuations, far out of statistics. This observation is a very mild form of anthropic principle. This is a form of anthropic principle that cannot be rejected even by those (like us) who most furiously oppose the use of anthropic-principle arguments in theoretical physics.

The point is:

1. Physicists like assuming we don't live in a special place in the universe, in space and in time.
2. But the fact that we are in a galaxy means we are in a very special place.  (Most points in the universe are not inside galaxies.)
3. The fact that we are on an earth at just the right distance to a star for life means we are in a very special place.
4. The fact that we live on land when 2/3 of the earth is water means we live in a very special place.
5. Etc...

So there are real limits in applying cosmological principle.  We don't always get the right answer if we assume it.  Sometimes we do have to accept this "weak" form of the anthropic principle that in order to exist we do need to be in a special place.

In a universe with the of value of λ like in our universe, it is quite reasonable that humans exist during those 10 or so billions years when Ωb and Ωλ are within a few orders of magnitude from each other. Not much earlier, when there is nothing like the Earth, not much later when stars like ours will be dying. Of course there is nothing rigorous in these arguments. But this is precisely the point: there is nothing rigorous or convincing in the coincidence argument.

So, to be alive we need to be in a special place.  We need to be in a galaxy.  We need to be the right distance from a star.  And so maybe we should not be shocked to discover we are also living in a special time when the Ωb and Ωλ are within a few orders of magnitude from each other.  These values are needed for life as much as existing inside galaxies or on warm planets is.

However, I admit we are not sure, and anthropic arguments are often not satisfying. (But again, philosophical arguments aside: not data suggesting anything like quintessence is real.)

Dark Energy As A Prediction Of General Relativity.

(This is the second post on my dark energy series.)

In physics, we have learned its best to write down theories in terms of Lagrangians or actions.  (See the GR one below).  We have also learned that you need to include every term in your Lagrangian consistant with the underlying symmetries of the theory.

For example, take the standard model of particle physics.  You take the known symmetries we observe in nature, SU(3)xSU(2)xU(1), and then write down every term comparable with this symmetry.  This is very important.  If you forget a term you get the wrong answer.

With this in mind, why would general relativity (GR) be any different?  Why would we not demand an action containing every term compatible with the underlying symmetries?

Going back to our paper we read:

The most general low-energy second order action for the gravitational field, invariant under the relevant symmetry (diffeomorphisms) is

And what is lambda?  Why, it is the cosmological constant.  The fact that you can add a constant means that you should expect too for the reasons stated above.

GR without a cosmological constant is what needs explaining, not GR with one.  And a cosmological constant gives rise to an effect completely akin to dark energy.  For this reason, a dark energy like effect should be thought of as a prediction of GR.

From the point of view of classical general relativity, the presence of the cosmological term is natural and a vanishing value for λ would be more puzzling than a finite value: the theory naturally depends on two constants; the fact that some old textbooks only stress one (G) is only due to the fact that the effects of the second (λ) had not been observed yet.

So if you accept GR, in a sense you should expect to see something resembling dark energy. Furthermore,

In gravitational physics there is nothing mysterious in the cosmological constant. At least nothing more mysterious than the Maxwell equations, the Yang-Mills equations, the Dirac equation, or the Standard Model equations. These equations contain constants whose values we are not able to compute from first principles. The cosmological constant is in no sense more of a “mystery” than any other among the numerous constants in our fundamental theories.

How true.  We play this same game with every other theory: we add every term, constant etc.., compatible with the underlying symmetries and and never complain.  Why complain that we would need to add one to GR?

Physically this is like asking: why are we therefore so surprised to see dark energy?

Are Prejudices Against Dark Energy Unfounded?

I want to examine several points by a recent paper Why all these prejudices against a constant? It isn't that this is the best paper on dark energy in the world, just that it highlights several issues relating to dark energy.

This first post is just to whet your appetite.  I start off quoting the paper:

“Arguably the greatest mystery of humanity today is the prospect that 75% of the universe is made up of a substance known as ‘dark energy’ about which we have almost no knowledge at all.”

This is the opening sentence of a (good) popularization article on dark energy. It is just an example, out of very many that can be found in the popular-science and in the technical literature, of how the ‘dark-energy’ issue is perceived by many scientists, and presented to the large public.

You know it is true, people make a big deal about how "mysterious" dark energy is.

We argue here that there is something scientifically very wrong in this presentation. There is no “great mystery”... This is a phenomenon which is clearly predicted and simply described by well-understood current physical theory. It is well understood in the context of general relativity, which naturally includes a cosmological constant. We argue below that the common theoretical objections against this interpretation of the acceleration are either weak, or ill-founded.

I agree with this assessment. As we will discuss in a future post, if you accept GR, it should be straight forward to accept a cosmological constant.  And a small positive cosmological constant would produce exactly something exactly akin to to the dark energy we observe!  So, I also think portraying dark energy as something incredibly bizarre is to be over the top.

It is misleading to talk about “a mystery” (not to mention “the greatest mystery of humanity”), for a phenomenon that has a current simple and well-understood explanation within current physical theories.

It is especially wrong to talk about a mysterious “substance” to denote dark energy. The expression “substance” is inappropriate and misleading. It is like saying that the centrifugal force that pushes out from a merry-go-round is the “effect of a mysterious substance”.

Again, interesting point.

So we will see.  I will post various points the author raises and let you decide.  Personally, I agree people put far too much mystery into dark energy.  In some sense, it is a prediction of GR. (As I will explain this claim in my next post).

We all accept GR right?  So, why do we treat dark energy as such a mysterious thing?

Posts in the series:
1. Dark Energy As A Prediction Of General Relativity.
2. Coincidence Problems and Dark Energy.
3. The 120 Order Of Magnitude Problem.

The Astronomist On The Dark Sector.

The Astronomist has a pretty good write up on dark energy or "the dark sector", highlighting the main ideas. (I encourage everyone to read it.)  He even has a derivation of the 10^120 order of magnitude problem and some hypothesis for what is going on.

Personally, I believe dark energy is just a cosmological constant.  I think this is what best fits the data.  We've measured w several times to be ~-1and more and the error bars just keep shrinking around that value. (For those who don't know w, or the ratio between pressure and density of the substance,  equaling -1 is the prdiction for dark energy being a cosmological constant.)

That said, we aren't 100% sure.  Moreover, as The Astronomist points out, if it is a cosmological constant we still need to understand why it is so small.  This is a major unresolved issue for physics. 

James Bullock in NC

I hear a professor of ours, Dr. James Bullock, was touring around the Tar Heel State. (Poor guy, he has to go from worrying about having beach sand on his heels to tar. yuck!)

Anyways, I thought I would upload some videos his graduate students have made public on this website to display some things he does.

Basically he studies galaxies and other large structures to better understand a variety of things. One thing his work sheds light on is the nature of dark matter. His work has been very important into helping scientists understand how warm/cold dark matter must be to have proper large scale structure formation.

This is what I was interested in, however, I am more interested in what things like supersymmetry tells us about dark matter so the theorists won me over. However, our theorists are working with him on viable dark matter candidates so I am still very interested in his research.

Here is a numerical simulation of galaxy mergers:



Here is a numerical simulation of how galaxies form:

Forget Global Warming: We Just Killed the Universe

There is a paper that has been posted on arXiv that has been causing quite a stir lately. It has even made it to the normal internet news services. Dr. Lawrence M. Krauss and Dr. James Dent, from Case Western Reserve University and Vanderbilt University respectively, have made the claim that by our observing dark energy we are affecting the life of the universe. Some news articles state it as "shortening" the life of the universe.

I tried to read through the article, but I'm not a particle physicist, nor a quantum mechanic, nor a cosmologist, but I'll give a crack at explaining it. So the idea is that in the early universe space was just as likely to decay into an unstable or metastable state that does not allow for matter, as we know it, to form or even for space as we know it to exist. But at some point the exponential expansion of the universe overcame the decay rate which is determined by a power law. Thus the universe began to grow faster than space will randomly decay, allowing for normal matter to form and for us to exist. But here comes the catch. If we observe the universe in some primordial state (i.e. observe dark energy) then the "quantum clock" of the universe gets reset and the universe reverts back to a state where the exponential growth and power law decay were roughly equal. Thus the universe reverts to a state where it is just as likely to decay as it is to expand. It follows that by our observing the universe in its most fundamental form we could conceivably cause it to decay into a state that does not allow for matter.

The problems with this are: What constitutes an observation? Do we have to observe the universe or does there have to be some interaction? in which case the observations are taking place all the time and our additional observing of the universe will not affect it any. From this point of reasoning we should assume that the universe is fairly stable (at least stable enough for us to be here, I think that is a very safe assumption) so I don't think there is anything that we can do that will significantly change the universe. The paper also mentions that it is difficult to make these assertions because they are based on quantum mechanics which doesn't really fit perfectly with gravity (GR) and when GR is taken into consideration things get sticky. Basically the only thing this idea can do is discount some versions of string theory and other unification theories.

So I hope that was a good interpretation of the paper. Let me know what you make of this paper.

University of Chicago Team Models a Type 1a Supernova

A team at the University of Chicago has announced the first successful computer model that replicates a type-1a supernova. They use the numerical code FLASH, which does fully compressible MHD along with Newtonian gravity. FLASH has been used on a number of other projects in stellar modeling and cosmology. In fact, if you wanted to model one of Joe's Population III stars, FLASH would probably be the way to do it.

What is especially significant about the Chicago group's accomplishment (aside from the really cool pictures) is that they have managed to make the star go supernova and completely blow itself up. Type-1a supernova are known by observation to completely unbind the star, leaving only an expanding shell of high velocity, super-heated stuff.

Type 1a supernova occur in binary systems where both stars have small enough masses to avoid core collapse supernovae. The first star ends it's normal lifetime by burning all of it's hydrogen and then all of it's helium in it's core. The core is then made of carbon and oxygen, but the star is unable to produce the pressures and temperatures needed to fuse carbon and oxygen. With the star's power source turned off, the star begin to contract under the pressure of gravity until the area around the core is hot enough for hydrogen or helium fusion. When hydrogen and helium ignite, it blows off the outer layers of the star and converts what is left into mostly carbon and oxygen, leaving only a carbon/oxygen core with no power source. This will contract under gravity until stopped by the electron degeneracy pressure if it's mass is less than 1.44 solar masses. So our binary system consists of a neutron star and a regular main sequence star and everything is happy for a while.

Things start to get exciting again when the second star nears the end of it's normal life and expands into a red giant/subgiant. Because the star has expanded so much, it's outer layers are very loosely bound by gravity and the white dwarf companion can begin to steal matter from the outer layers. As this matter is deposited onto the white dwarf, it's mass increased until it approaches the 1.44 solar mass limit. Before it hits the limit, however, temperatures and pressures inside the core hit the point where carbon fusion begins and a runaway burning of carbon and oxygen occurs. Essentially, the star burns all of its carbon and most of its oxygen all at once creating a huge explosion that blows the star to bits.

The University of Chicago team has modeled this process. You can find some really cool movies here. This is especially important to cosmology, because type-1a supernovae are thought to be standard candles and are one of the evidences for dark energy. If the Chicago team can find ways to make the output of type-1a supernovae vary, it will cast doubt on their support for dark energy. On the other hand, if there turns out to be only one way to get the supernovae to blow up that is consistent with observations, this would go a long way to settling the debate of the type-1a supernova measurements of dark energy.

Musser's 10 Predictions by 2017

George Musser works for the Scientific American. He recently made a prediction of what he expects to see discovered in physics over the ten years.

Though they are just predictions, the fact of the matter is these predictions are all theoretically possible to have via the LHC at CERN, the Plank Satellite, Ligo, Lisa and other experiments going up over the next decade. If all goes well most and maybe all ten of these may in reality happen! We really are living in an interesting time in physics. Here is his list:

1. HIGGS
2. SUPERSYMMETRY
3. WHAT DARK MATTER IS
   
4. DARK ENERGY
   
5. HOW INFLATION HAPPENED (ie... was it an eternal inflation model or other)
   
6. GRAVITATIONAL WAVES
7. PROTON DECAY
8. LITTLE BLACK HOLES (Formed in particle accelerators)
9. ANTHROPIC PRINCIPLE (How the Universe began, like #5. String Landscape?)
   
10. OTHER EARTHS (Other earths with life. This one is the most far fetched but who knows)
    

Only time will tell. I hope to be working on a few of those at graduate school.

What Would I Like to See in Graduate School?

As many of you may know I hope to be off to graduate school next year. If I am like the average graduate student I will be there 5-6 years meaning I may be there until 2012-2013.(Yikes!) I happen to be going at perhaps the best time in history. In the next 5-6 years we may come up with some of our most profound discoveries ever. Here is what I hope to see.

1. The Higgs field and Supersymmetry: We all have been thankful for the success of the Standard Model, but I believe we are ready to move on. One major particle that I am desperately hoping CERN finds is the Higgs Boson. Come 2007, the LHC, at CERN will be operating at energies higher then currently being achieved anywhere else; on the order of of 14 TeV. In addition to finding the Higgs, I am really crossing my fingers that we will find strong evindence for supersymmetry. Not only will supersymmetry give us a huge slew of new particles to explore, it will hopefully resolve some of our issues such as the vacuum energy problem and candidates for dark matter.

2. Gravitational Waves: Being able to detect light we cannot see visually, like infrared and microwaves, has greatly furthered our understanding of nature. I hope we will soon add to that gravitational waves. Gravitational waves will greatly enhance our ability to study the universe. We will better understand centers of Galaxies, neutron stars and black holes. In addition, many are very excited on what light gravitational waves will shed on the initial stages of the universe. That will help us further understand not only large stellar objects, but also the small particles which formed in the early stages of the universe. Hopefully LIGO and LISA will be successful which I am at graduate school.

3. Neutrino Background: Many are familiar with the CMB or cosmic microwave background radiation but not as many people are familiar with the theoretical neutrino background. It turns out, there should be a huge collection of neutrinos left over from the big bang era which haven't interacted with anything. We should be able to study this collection much as we can study the CMB to determine truths about the universe. Surely there will be much learned from the neutrino background, and this is yet another discovery I hope we make soon.

4. Pop III Objects: Stars and planets today have lots of elements heavier then hydrogen and helium. During the initial stages of the universe, it was practically all hydrogen and helium. Because of this the physics of the cosmos was very different then it is today. These differences make all the difference in the world if you are trying to understand the universes history. Understanding the universe's history is very important in uncovering how and why the universe is the way it is. Hopefully the Hubble, or more realistically the new James Webb Telescope which will launch in 2013, will detect these objects.

5. Dark Matter and Dark Energy: This may be asking a little much, but with some luck the above things will set straight what is dark matter and dark energy. Maybe supersymmetry is responsible, or maybe something else.

6. The Stage Set for the Theory of Everything: Okay, I have to realistically believe quantum gravity, etc... will not be solved in the next 5-6 years. However, if we can understand the basics of supersymmetry, information coming from gravitational waves, the neutrino background, early population III objects and the higgs field, we might be able to have enough cosmological data to really get somewhere. I've said it before, and I will keep saying it, string theorists are demanding particle accelerators the size of the solar system to test things that will result in understanding quantum gravity. We may never have such accelerators, but we do have an event about 13.7 Billion years ago with energies high enough that if we could examine it close enough we may be knocking on the door to understanding quantum gravity and more. These are the events I hope to see which I believe will lead up to that.