A simple and short discussion on "Dark Matter".
Date : 12/12/2014
Version: 0.8
By: Albert van der Sel
Status: Ready.
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Some nice theories from physics... Let's explore "Dark Matter"...
Contents:
Chapter 1. Introduction, and scope of this note.
Chapter 2. "Brane World" scenario's (2 & 3).
2.1 The older "Brane World" models.
2.2 The newer (Randal/Sundrum) (3+1) "Brane World" model in (4+1).
2.3 Discussion of a representative article: "A new Dark Matter candidate in Low-Tension Brane Worlds".
2.4 Is a "Brane-World" detectable? And what about Planck scales?
Chapter 3. Single "Traditional" Universe model.
3.1 The Standard Model matter (the common stuff).
3.2 Terms to know about: Cold- and Hot dark matter, baryonic- and nonbaryonic dark matter.
3.3 The Axion: a nice Dark Matter candidate in the "Traditional" Universe model.
3.4 The Neutralino: a less likely Dark Matter candidate in the "Traditional" Universe model.
Chapter 4. Dark Matter and Inflationary Theories.
4.1 Short intro on Inflation.
4.2 Inflation and some ideas on Dark Matter.
As an "abstract" of what you can expect here:
- Multi dimensional "Brane World" scenario's have the potential (and actually do so) to put forward "dark matter" candidates,
like the "branon", as a result from Brane tension, and fluctuations, in the "bulk" (see chapters 1 & 2).
- More (traditional) single Universe theories, especially using parity/symmetry considerations, have lead to the "axion",
a particle that might be considered to be a real world "dark matter" candidate (see chapter 3).
Other "WIMPs" are explored too, like the "neutralino".
- As the last part of this note, considerations from Inflationary theories are explored, to see how they might contribute to
dark matter discussions (see chapter 4).
Chapter 1. Introduction, and scope of this note.
A true comprehensive (universal) theory, will certainly account for both "dark matter" and "dark energy" in the same theory.
Unfortunately, we don't have such a complete theory yet. But there already exists some elaborate theoretical frameworks.
I like to start with the focus on just one of these two phenomenons. Let's start with "dark matter". "Dark energy" is something for another document.
If you would have told a physicist, say, in 1975, that about 85% of all matter is "dark matter" instead of the Standard Model matter (the "common stuff"),
he/she probably would have first stared at you for a short moment in total amazement, before deciding that you are really in need
of some psychological help.
Dark matter is strange stuff indeed. Already in the 1920's of the former century, just a few astronomers argued that there should
much more "mass" in the observable Universe, but which was not accounted for in observations. Or, stated somewhat differently, could not been seen...
The idea "slumbered" along the minds of some physicists and astronomers, over all those later years, but never stuck firmly.
Then, say, about 20 years ago, rather suddenly, a revived interest grew, and got stronger and stronger as time passed.
There are good reasons for that. Some new observations, and revised interpretations thereof, strongly suggested that additional mass just have to exists.
In addition, some newer, pure theoretical considerations, pointed towards that same conclusion.
Note on observations:
So, quite a few astronomical observations lead us to believe that there exists a lot of "unseen" or "dark" matter. For example gravitational lensing
is such an observation. However a real strong one, is the discovery that the stars and matter that live in the disk of a spiral galaxy (a milky way)
rotate with more or less the same velocity around the center. This was not expected at all. If you take a look at our own Solar system,
the planets move in orbits in accordance to Kepler's laws. for example, the inner planets move much faster that the outer planets.
It was expected that stars and matter close to the center of the Galaxy, moved much faster. But they do not.
Vera Rubin, a female astronomer, was the first to publish a study of such content. It disclosed the discovery that most stars in spiral galaxies orbit
at roughly the same speed. Initially, this did not ringed the bell very loudly in the scientific community. However, progressively, the discovery was more and more
confirmed by others. It led the astronomical community to believe that much more (unseen/dark) mass had to exist outside the Galaxy's disk.
One famous characteristic of "dark matter" is, as we see it today, is that it does not interact with electromagnetic radiation.
So, it is "transparant". It only has gravitational effects on normal matter and radiation.
So, photons (or electromagnetic fields), does not interact with it, while "normal" matter does (like for example EM radiation affects electrons and protons).
If you believe that, then it follows that "dark matter" is (almost?) completely transparant for EM radiation, like light.
Thus, it's un-observable using, for example, telescopes. We simply can't see it. However, there might be ways to detect it, for example, in signatures
from collisions using particle accelerators (like the LHC at Cern).
One strong candidate is the "axion". For now, it is still a hypothetical particle. Although the axion is still an illusive particle, it is
"much closer to home", in comparison with other candidates from Multi-dimensional "Brane World" scenario's (like "branons").
To investigate "Dark Matter", and where it comes from, 4 main directions of thoughts can be distinguished:
- An approach using a single (traditional) Universe model, using "mundane" but (yet) undetected matter. For example, the "axion" particle.
- A Multi-Universe approach using "Brane Worlds" and other results from M Theory/Superstring Theories.
- A "Brane World" scenario, where the Brane has some interaction with the Bulk, often using a (3+1) Brane in a 5 dimensional Bulk.
- And, following what physicists/cosmologists have found, while exploring "inflationary theories" (pre Big Bang phases).
Following (1), more mundane explanations were devised, like particles we do not know of yet, which would account for the additional mass.
Or, certain heavy relatives of particles we already do know (e.g. neutrino's), but we still have not found those heavy relatives yet.
Often, these unknown particles are generally classified under the name of "wimps", which is short for "weakly interacting massive particles".
The "weakly interacting" part then, should make it clear that the common forces/fields we are familiar with (like the electric/magnetic force),
has no influence on dark matter. However, the "massive particles" part, shows that gravitational effects is just a very
characteristic feature, if you got really really a lot of those 'whimps' throughout the Universe.
We will come back to this sort of interpretations later in Chapter 2.
Anyway, we will see how physicists & cosmologists think about reasonable explanations of "dark matter", including cold- and hot dark matter, wimps,
and exitations from brane-world scenario's.
Now, I will start the dark matter discussion with the type (2)/(3) approach, thus using "Brane World" scenario's. This is quite exciting, really!
Personally, I like those most.
But, attention to (1) and (4) is absolutely mandatory too, since certainly not all physicists/cosmologists are "Brane" enthousiastics.
Surely, the inflationary theories, they all know multiple and complex phases, and some may have produced non-baryonic matter.
And for the more traditional (mundane) "one Universe" approach, a particle like the axion might be very promising.
Chapter 2. "Brane World" scenario's (2 & 3).
2.1 The older "Brane World" models.
At the beginning of Brane World scenario's, around 1990 (plus/minus a couple of years), it's fair to say that the original notion
of a Brane (or n dimensional manifold) was used in respect to a 11 dimensional M-Theory, using compactification of the extra spatial dimensions.
However, around 2000 (plus/minus a couple of years), the model shifted significally, now to a (3+1) Brane (our Universe) in a 5 dimensional space.
The number of 5 is not really mandatory, but is simply often used in later arcticles, either for simplicity, or in accordance to Kaluza Klein, or in accordance
to idea's of Randal and Sundrum.
Let's start with the original model. In later sections we get plenty of time to look at the more modern 5 dimensional models (without compactification).
For that, please see section 2.2.
A partly succesful modern theory of physics, is called "superstring" theories. Essentially, elementary particles are described as "vibrating strings",
on an extremely small scale (in the order of 10-35 m), but thereby still are avoiding the classical concept a "point" particle,
(a "true" point was never appealing to physicists anyway).
The variety of stringtheories, often required different extra spatial dimensions. However, generalizations led to a consensus of a total of 10 dimensions,
of which (x,y,z,t) can be viewed as our regular SpaceTime, and 6 additional, compactified (curled up) "hidden" dimensions. The term "hidden" is used
due to the fact that the metric of those "extra" dimensions is so extremely small (10-35 m), that effectively, they are completely undetected indeed.
M-Theory is generalization of different stringtheories, and unites them, using an addition of one additional extra spatial dimension.
So, in M, we are left with the regular (x,y,z,t) SpaceTime and 7 hidden/compactified additional dimensions. Thus in total 11 dimensions: time plus 10 spatial dimensions.
Don't get confused. "Space" still just looks 4 dimensional, but (so to speak), zoomed in into an extremely localized region, would then show
those very compactified curled-up extra dimensions.
If you are new to this, then an analogy might help. Consider a long one-dimensional line. Suppose that it would be possible that you keep zooming in.
Then, you might ultimately find that it's actually a stretched "cilinder".
So, from a macroscopic perspective, those additional dimensions, were so small that they could not be detected.
That's why the streched long and very small cilinder, just appeared to be no more than a line.
However, it's important to note that the very small metric of those additional dimensions, is like a Kaluza-Klein approach.
Many theorists in the field nowadys, do not "a priory" demand such small scales are always mandatory, at least not for all of them. It might be even so,
that such a metric is in the cm scale. That might even hold for just one of those extra dimensions.
And... if it goes undetected..., it simply goes undetected! For example, suppose only 'gravity' is 'aware' of such an additional (large) dimension?
Then, for example, the Electromagnetic interaction, the strong nuclear force etc.., would not know of such an additional degree of freedom.
Especially a successful article by Randal and Sundrum (1999), using a 5 dimensional space only, with no compactified dimensions, lead many theoretical physicists
to explore Brane World scenario's from such a scenery. More on this later on (section 2.3). But, let's go back to the first, initial thoughts.
M-Theory also uses "Branes", which are n-dimensional "manifolds". And ofcourse M-Theory uses strings. The strings can be "open" or "closed". If a string is closed, it forms a loop
(like a circle). One common interpretation is, that if string is open, it is bound to the "brane" (it's endpoints are on the brane).
Often, in many illustrations, a Brane is visualized a just a 2 dimensional plane.
However, "our Universe" (our World) then should be a 3-Brane with respect to spatial dimensions. It would be a 3+1 Brane when "time" is taken into account too.
Fig 2. Illustrating a Brane, and open- (tied to the Brane), and closed strings.
One great interpretation (or hypothesis/speculation) goes a step further. Now, the "normal matter" we know of, is bound to it's own "world",
or, in other words, bound to "the Brane". This matter is thus synonymous to the open strings, with their endpoints on the Brane.
Some closed strings however, are not tied to the Brane. They have no endpoints on the Brane.
For example, it is "suspected" that this is true for the "gravition" (a closed string), which thus might even "leak out" from the Brane.
Please be aware that these are not proven facts. It's just all theory for now, but certainly one where many physicist place their bets on.
It's very tempting to suppose that the extra dimension(s), would sort of "dillute" gravity. It could well explain why gravity is so weak
on smaller scales, like particle interactions.
The Universe, could be a "Multiverse", in the sense that more Branes would exist. In a way, a certain Brane might have it's own
vacuum properties, types of particles, physical "constants" (like speed of light?), amount of mass etc... etc...
Sure, it's hypothetical. But, especially theoretical physicists and cosmologists pondered about those models, and tried to make
any sense out of it. Now, if a model makes sense, it could well be a true candidate for a real theory.
Ofcourse, if all spatial dimensions, except the 3 we know so well, are compactified, then it's not easy to see that there could exist
seperate branes, separated by some "distance". This is also why the theories of Randal & Sundrum, where dimensions did not needed to be
curled up anymore perse, were greeted with much enthousiasm.
Fig 2. Illustrating the "Brane World model", with multiple Branes, and open and closed strings.
Now, with respect to "dark" (invisible) matter", the following intuitive line of reasoning might be followed.
For simplicity, often just one additional special spatial dimension, say "z", is considered.
Multiple Branes (in this model) could then be seperated from each other, along the "z" direction.
Usually, physicists in this field say that the Branes live in the "Bulk", which is this not fully understood stuff, which
seperates the Branes.
Or, you keep all dimensions in place, and the Bulk is just a "d" dimensional wonderful place.
Now, since gravitation on short distances between small particles is almost "0", compared to the other fundamental forces
(like for example the electromagnetic force between charged particles, or the very strong nuclear force), already quite some time ago,
some physicists suspected that gravitons were "somehow" able to leak out from our Brane, into the Bulk.
See section 2.2 for a newer version of how physicists deal with dimensions in the Brane and the Bulk.
Ok, suppose for now, that only gravity (gravitons) is 'aware' of that one special spatial dimension.
Or, to say it otherwise, from all normal matter (fermions) and force carriers (bosons), only gravity is able to use, or to interact,
with the z dimension. You might thus say that gravitons can use the Bulk as an extra degree of freedom.
In this line of reasoning, gravitons might (more or less) freely move from Brane to Brane, and thus it might follow, that an observer
in such a Brane might notice much more gravity (or unseen mass), than can be accounted for, from the normal matter that can be observed.
Would a model like that, could help explain the gravitational effects that is usually attributed to "dark matter"?
Well, this simple model is actually.... too simple ! It's not quantified in any way, and there is no further basis except for some assumptions.
However, what we see from this, is that certain effects in our manifold (or Brane), could originate from outside our Brane.
Now, that is an interesting point.
Ofcourse, it's playing around a bit, as a sort of preparation. In the next subsections, let's take a look at a few serious models.
In some serious scenario's, it's the actually the intrinsic fluctuations (or effects of a natural tension in the Brane), which give rise
to additional particles, but which do not "couple" to ordinary matter in the usual way (for example, through the electromagnetic interaction).
However, since those particles are thus assumed to exist, and mass-energy is associated with them, they are a candidate for being the "dark matter" constituent.
That they are indeed candidates, can be made likely if it can be proved that they do not interact with "normal" matter, and thus are "dark".
Note that such a scenario does not use multiple Branes. We will touch on such a scenario in section 2.3.
As a completely different (but shortlived) scenario, in the past, a few physicists even considered the following model (which has been abandoned by now).
Suppose the tension in a Brane is so high, compared to a fluffy Bulk, that the Brane is almost like a "defect" in Bulk space.
Quanta in the Bulk tried to interact with that "defect" which might even have been in such a way that ocillations arose "in" the Brane,
which equals the particles as we observe them today. However, such a model did not hold.
But, it's an example of how far we are willing to explore...
2.2 The newer (3+1) "Brane World" model in (4+1).
There are quite a few Brane Worlds models actually. It's certainly not only based on M-Theory with compactified dimensions.
Actually, modern ones are based on the Randal & Sundrum model, which is a (3+1) Brane in a 5 dimensional Bulk.
There are many articles out there, but in 1999 a remarkable one appeared:
"An Alternative to Compactification (1999)", which can be found here.
Essentially, the authors describe a single 3-brane with positive tension, embedded in a fivedimensional Bulk spacetime.
Using "gravity" as the vehicle to explore the scene, and using wavefunctions, they argue that a graviton in the Bulk neccesarily
will be in a confined bound state. Initially, they make no assumptions on the additional spatial dimension rc, so
it could be compactified. Using math and letting rc grow to infinity, they manage to keep the "four-dimensional effective Planck scale",
to go to a "well-defined value" as well.
This means that a consistent 4 dimensional theory of gravity can be derived from a 5 dimensional model of gravity.
It might not be totally clear why that is so, but I pospone that a bit for section 2.4.
Such a 5 dimensional model, using no compactification, is a remarkable deviation from M-Theory based models.
Secondly, the bound state of the graviton as described in this article, actually means that they are close to (or near "at") the Brane,
and do not travel "freely" around.
Note that, in simple words, we can now speak of "distances" along that fourth spatial dimension. If you would insist, you can still use
more compactified dimensions. However, the one that (probably) only gravity is aware of, is that fourth spatial dimension.
Fig 3. Illustrating a newer "Brane World model".
Also note that "the hyperspace" here is (4+1), meaning 4 spatial and one time dimension. A Brane then would be (3+1).
It's important to note that variants to this model exists, with a large extra dimension, while still having other compactified dimensions.
2.3. Article: "A new Dark Matter candidate in Low-Tension Brane Worlds".
Let's discuss a serious scientific article, which addresses "dark matter". It's called:
A NEW DARK MATTER CANDIDATE IN LOW-TENSION BRANE-WORLDS
It's an article from "www.slac.stanford.edu", namely SLAC-PUB-10933, which can be found here
Ofcourse, countless articles have been published up to this date, but this one (from 2004) is rather nice in my opinion, to illustrate
a specific (classical) modern Brane World scenario. Note that this article does not rely on multi Brane scenario's,
but instead discusses the Brane tensions, which is responsible for generating particles. If those particles do not couple to
ordinary "Standard Model" particles, we may have found a Dark Matter candidate.
These sort of articles are indeed hard to read and understand. I will try to give a short understandable "discussion" (as far as I understand it).
Discussion:
It's a "single" Brane model only.
Again, it assumed that the (ordinary) "Standard Model" particles (the ordinary matter: quarks, leptons) are confined to their Brane,
as they are open strings. Closed strings, in particular the graviton, can move (or leak out) to the Bulk.
But here, the emphasis here is not on "leaks to the Bulk", as it is here actually focussed on the dynamics of the Brane itself.
It's further assumed, due to good reasons, that Branes have a certain "tension distribution", which can be viewed as oscillators.
You may compare it to "stress-energy" which we can find in nummerous fields in physics, like fluid dynamics, relativity etc.. etc..
Such "stress-energy" might be interpreted as a flux or density of energy, in fact..., due to continuous "changes".
Now, also due to relativistic considerations seen over the metric (distances), the Brane releases energy, which is quantified in particles.
That is not so strange, since in Quantum Mechanics, energy absorption and release is always quantified, in quanta, or particles.
These particles are called "branons", with a clear reference in their name as to theirs origin: generated by Brane oscillations.
Most folks interpret the article in this way, that the fluctuations of the Brane are in the extra dimensions.
The creation of particles, or fields, from a fall of potential energy, is not new. For example, in certain inflationary theories,
it is argued that at a certain point, the false vacuum potential (top of the "mexican hat"), has dropped, which generated the Higgs field.
Also, closer to home, a transition from a higher quantum state to a lower quantum state, might produce a "free" quantum, like a photon,
which is quite a common event in atomic physics. There are many more examples to illustrate the key point.
The article is also partly based on the classical article from R. Sundrum (Phys. Rev. D59, 085009), called "Effective Field Theory for a Three-Brane Universe"
which can also be found here.
This article, decribes the dynamics of “3-brane”, which fluctuates in a higher-dimensional, gravitating spacetime (the Bulk).
Sundrum shows, that bosonic fields may arise in the 3-brane, in a background of the Bulk metric. But that article covers much more than that.
Under the assupmtion that "branons" do exist, it's now up to the authors to prove that they are "massive" and "dark".
For the latter, it means that branons have no, or neglegible interaction, with ordinary matter.
They try to do that by pondering on the equation of how branons would interact with Standard Model particles. As a result, it happens to have
a term 1/f 4 (where f is the tension in the Brane), thus meaning a very strong suppresion of that interaction.
In the same process, they show the branons are massive.
For an intuitive explanation for the strong suppresion: the branons are "sort of" strongly tied to the fluctuations themself, making their interaction
in the Brane with Standard Model particles negligible, except for their large mass, which can be noticed by the effects the astronomers see today.
Hence, a "dark matter" candidate (the branons) is proposed, from a Brane World scenario.
2.4. Is a "Brane-World" detectable? And what about Planck scales?
1. Detecting Branons, KK gravitons (brane fluctuations/ocillations):
Since articles like shown in section 2.3, have good grounds to propose "branons", we might even try to detect them, using current accelerators and methods.
That is, if we know what to look for. This is not a silly remark.
Remember the discovery of the Higgs boson at the LHC in Cern? Once seen as an extremely elusive "particle" (or field), they managed to detect it after all.
Anyway, I guess what I want to say here is that they indeed discovered Higgs, using certain models, decay channels, lots of derived data etc...
In fact, in the end, those folks at Cern knew what to look for.
Branons could be "true" or virtual particles, that's not fully clear now (if they would exist). And branons have competition, for example with KK-gravitons!
As you remember, branons are the result of ocillations (or fluctuations) of the Brane in multi-dimensional space.
They have an almost negligible interaction with normal Standard Model matter.
In an article like "Brane-Worlds at the LHC: Branons and KK-gravitons", which can be found here, the authors
argue that with our present day accelerators, and new carefully designed measurements, it could be possible to witness events
where energy is "missing", thus not accounted for, or that some momentum component is completely unexpected, or missing.
Then, if the theoretical calculations would match those results, it might be concluded (or better "suspected"), that dark matter particles might have contributed
to account for the missing values. It's a good idea really.
The article mentioned above, is really hard to read, as is true for most of those articles. But the statement above is actually the most important
conclusion of the authors.
2. Search for Microscopic Black Hole Signatures:
It will not be "direct", conclusive evidence. But, if found, it will be a strong point for Brane and/or string theories.
At proton-proton collisions at the LHC (Cern), where energies are around the 7 TeV range (or higher), enormous amounts of data is produced.
Some researchers, plough through that data to search for "Microscopic Black Hole Signatures", that is, can we find some data that supports
the fact that Microscopic Black Holes were produced?
Note: by the way, such research also takes place with Ultra-High Energy Cosmic Rays.
An important idea is, that a larger hidden spatial dimension, would sort of "dillute" gravity, and would explain why gravity is so weak,
at for example particle interactions.
If indeed a hidden spatial dimension is "large" (much larger than 10-35 m), this sort of "lowers" the Planck scale (in terms of energy),
where the magnitude of the gravitational force becomes comparable to other forces.
This could mean that, if in an accelerator particles collide with an Energy as low as 10 TeV (or so), the particles might get near enough
for gravitation to get a strong effect. Still closer, would mean a very high gravity, where that small region might collapse into
a socalled "microscopic Black Hole". This is not my idea: it's from expert physicists who see it as a possibility.
Anyway, if thus "microscopic Black Holes" would be produced at the LHC (or other accelerator elsewhere), and those footprints would be detected,
it would be an indicator (not a proof) of "a larger hidden spatial dimension". Thus, that would mean a plus for the realism of Brane Worlds theories.
Conclusion of Chapter 2: As shown sofar, especially in section 2.3, Brane World scenario's have a true potential
of providing "dark matter" candidates. So, indeed, a "potential" sure..., but nothing has been proven sofar (december 2014).
Chapter 3. Single "Traditional" Universe model.
Here we do not pay any attention to "Manifolds/Branes" that live in a sort of "Hyperspace/Bulk". Also, we do not get into Inflationary theories yet.
Although lots of theoretical physicists and cosmologists are positive on Brane World scenario's, certainly not all of them
are equally enthousiastic. Especially the fact that Brane World scenario's are still completely theoretical, makes a lot of scientists
want to stay "closer to home".
Many of them like to investigate more "mundane" explanations, like for example, an elementary particle that we do not know of yet.
Ofcourse, it's not really mundane, but it's probably more "traditional" compared to Brane World scenario's.
So, what has research yielded sofar?
Let's first see what the building blocks are of the regular Standard Model matter (the "common stuff").
3.1 The Standard Model matter (common stuff).
Fig 4. Illustrating in a high-level view, the known "Standard Model" elementary particles.
There exists hundreds of elementary particles (like proton, meson, pion etc..), but they are not really "elementary", since they are
"composed" from (what we think are) the true building blocks: quarks and leptons.
So a proton, is not a truly fundamental particle, since it consists of three types of quarks (see section 2).
If you would take a look at section 1 of figure 4, you see the sorts (or flavours), of quarks and leptons.
Figure 4 is not complete, since I left out the anti-matter relatives. And for the quarks, it is true that there exists and additional sort
of "color charge" property, which is not shown in figure 4 either. However, for our purposes, figure 4 is good enough.
So, the "true" elementary particles are the fermions (which are quarks, leptons, antiquarks, and antileptons), where quarks and leptons form
the composite "matter particles", and the antiquarks, and antileptons form the composite "antimatter particles".
No need to fully remember this. However, in many discussions these names will probably come across, so it helps if you have a sort of
(very) high level of overview of "Standard Model" matter.
Apart from "matter", we also distinguish various "force carriers": the bosons. So, the "strong nuclear force" uses gluons as
the force carrier, and for example, the photon is the force carrier for the ElectroMagnetic force.
Bosons are a bit "virtual" stuff, since we usually speak of a force field, but when the field actually interacts with matter,
the corresponding Boson "materializes" (sort of).
Sometimes the term "baryonic" matter is used in discussions. That's simply composite matter made of the quark stuff, like the well-know protons, neutrons
and many others. It's actually not such a good term like "fermion" is. But, the term stuck around, and you are bound to see it in other discussions.
3.2 Terms to know about: cold- and hot dark matter, baryonic- and nonbaryonic dark matter.
You might read other notes on Dark Matter as well, and thus it is important to know of a few important "terms",
like "cold" and "hot" dark matter, and "baryonic" and "non-baryonic" dark matter.
Baryonic- and Non-baryonic dark matter:
Baryonic matter then, is actually normal (standard model) matter as you already have seen in section 3.1.
So, stars, dust, planets, us..., is baryonic matter.
But in "dark matter discussions", there is just a lot of it that goes undetected for now. At least, that's the assumption then.
Well, this candidate then escapes the usual characteristic of dark matter, which is that it does not interact with Standard Model matter,
except for gravity (and possibly the nuclear weak interaction). It is just Standard Model stuff itself !
We have seen the class of "baryonic matter" already in section 1.2.1. Just take a look a few lines back. So, "baryonic dark matter" then
is "normal" matter. You might think of extremely faint stars, that go undetected. Or, MACHO's (Massive Astrophysical Compact Halo Objects),
that exists outside the disk of a spiral Galaxy. Again, those might be brown dwarf stars, extremely faint stars, or objects which did not "make it"
to start their live as a star (like Jupiter-like gas planets) etc..
However, it's unlikely that those are the real dark matter constituants, but it has not been ruled out completely yet.
The non-baryonic matter might include the "common" leptons (see section 3.1), but in dark matter discussions, that's usually not the case.
Instead, people talk about "axions", or "supersymmetric particles", and some others, which are (hypothetical) unknown, undetected particles up to this date.
It should be "stuff" that's not discussed in section 3.1, and not shown in figure 4.
Indeed, at the nuclear "strong interactions", from chromo dynamic theories, there might be "room" for yet not fully understood "parity violations", which might result
in "axion" creation.
We will see about those cadidates in the next section.
This section has the sole purpose to introduce some "common terms", which you may see in other dark matter discussions.
Hot dark matter and Cold dark matter:
This is just no more in a differentiation in the relative speed of the dark matter candidates.
"Cold" means very slow moving stuff, compared to the speed of light. You can imaging that cold unknown stuff, might form heavy (transparant) clouds,
or forming "lumps" in some hierarchical way. Since gravity still "works" with dark matter, that's not a silly assumption.
However, large "lumps" should ultimately "collapse" (?), and it's not solved what the evolution could be of such "stuff".
"Hot" means that we have particles, zipping around with the speed of light (or very fast anyway). So, this will not form "lumps".
You might say that such unknown particles behave "like" neutrino's. They have rest mass and move with "c".
"Hot" dark matter was never very appealing, while "cold" is. This is so, since "cold" dark matter may form "lumps" or "structures"
which are very heavy, and thus may account for the astronomical observations.
3.3 The Axion: a nice Dark Matter candidate in the "Traditional" Universe model.
The "axion" could well be a serious candidate!
A similar scenarion from the past... the postulation of the neutrino.
We have seen it before (a long time ago, around 1930), that a particle was "postulated" for good reasons. This was the "electron neutrino", or in short, "neutrino".
The postulation of the neutrino, namely resembles the postulation of the "axion" quite closely. That is, not exactly, but closely.
The neutrino (a "neutral" lepton as you can see from figure 4) was first postulated in 1930 by Wolfgang Pauli.
He tried to explain why the electrons in "Beta decay" were not emitted with the full reaction energy of the nuclear transition.
That process namely, "looked" at first like a violation of conservation of energy and momentum.
Beta decay is quite common, and can happen in Atomic nuclei. It's the result of the socalled "weak interaction" (but that is not important right now).
For example, a free neutron might "decay" into a proton and electron. However, the energy balance then, is not OK.
n -> p+ + e-
In this case, energy and momentum is "missing". Why does not have the electron the full reaction energy?
Therefore Pauli (later Fermi) postulated a light, uncharged particle, the neutrino, who "took", or accounted for, the missing energy/momentum.
n -> p+ + e- + neutrino
This time, the balance is alright! The neutrino takes the missing energy/momentum. In 1956, the existence of the neutrino was indeed experimentally verified.
The sole key point here is, that a at first "strange" phenomena (missing momentum), was explained by a introducing a new theoretical particle (maybe a bit daring..),
but was succesfully found later on. So, it all made sense afterall.
Ok, let's return to the Axion. For now, I like to call it a "QCD Axion". You may view the QCD Axion as being a "WIMP", like we discussed in Chapter 1.
If QCD axions exist, according to theory, they are extremely light, very weakly coupled to Standard Model matter, and very long-lived. The "extremely light" part
might initially not look good for a Dark Matter candidate, however, enormous quantities would compensate for that. Actually, if you would visualize it as a "field",
then automatically, you might "see" it as a "large" distribution of mass, and that might accomodate the astronomical observations.
And, other good news is the "very weakly coupled to Standard Model matter" part. That sounds very good too, since that means... "dark" !
Indeed, there are theoretical considerations, that makes the QCD axion similar, or "looks like", a Higgs boson scalar field, which is everywhere.
However, we probably would like to see some "lumpy" characteristic too, so that it can explain "gravitational lensing" too.
This is not yet entirely solved, I believe.
How did the physicists actually came to the "Axion" particle anyway? Let's try to explore that. It's not that simple, but walking through
a number of examples from physics, will let us get there.
3.3.1. Parity and Symmetry Violations:
Quantum Chromodynamics (QCD) is a very important theory, or framework, in elementary particle physics.
Especially, the "strong nuclear" forces is under study. Take a look at figure 4 (section 3) again.
There are two things we must put our focus to: Beta decay (weak nuclear), and "quark-gluons-quark" interaction (strong nuclear).
Sometimes, we "expect" a sort of "symmetry" violation, and when it's not observed, it can be a bit disturbing.
Not always ofcourse, but if a theory is succesfull on a "weak variant", but we don't see it at a "strong variant", then something might be missing or wrong.
Example 1: Electroweak Baryogenesis.
For example, it is assumed that at a certain phase at the Big Bang, particles were created. It's only natural to assume that matter and anti-matter
were created in equal measures. But that was not entirely so. There is a portion of regular matter "left over". So, it seems as if there existed
some sort of "bias", or asymmetry, but what was that? How did it operated? We are not fully sure yet. But I like you to focus on that "asymmetry" only.
Sure, there are a few theoretical models. One possible mechanism, displaying such strange "bias" might be the following:
The b-quark has a tendency to "weak-decay" into its antiparticle, the banti-quark. But, in that process, the left "spinning" orientation, will be switched to
to a right "spinning" orientation. Such a switch, which is not "mirror" consistent, is called "Parity Violation".
To make it worse, it has been observed that the banti-quark is more likely to decay into the b-quark than it is for the b-quark to decay into the banti-quark.
This is a strange sort of "bias". It's not symmetric. But, it was involved in a process called baryogenesis, and is likely to have contributed for the fact
that the "common stuff" is composed of matter and not antimatter.
Example 2: Weak interaction is "biased": "CP Violation".
One remarkably asymmetry is, is that the "weak force", seems to have a sort of "preference", as if the "dices" it uses, are biased.
let's take a further look at theories, or phenomena, which are invariant under "transformations".
One certain transformation is "mirorring" which creates the mirror image of a physical system, comparable to what an ordinary mirror does.
It's referred to as "Parity (P) symmetry". You may also see this Parity (or space inversion) as the reflection in the origin
of the space coordinates of a particle or particle system. This inversion should not change the interactions between the particles in a fundamental way.
With all physical events observed until the fifties of the former century, the symmetry seemed to have really worked !
For example, ElectroMagnetical events, obey P symmetry.
A second rather special operation is "Charge conjugation". Here, in a physical system, we would replace every particle by it's anti-particle,
and the net result should be, that the fundamental interactions do not change at all. That is, if we think we know all properties of a particle.
For years (until the fifties of the former century) it was assumed that charge conjugation and parity were symmetries in effect in elementary processes,
determined by the electromagnetic, strong, and weak interaction. For example, if you mirror a nuclear process, the same effects are observed.
However, it turned out not to be true.
If an event violates Parity, or Charge conjugation, it's referred to as "P violation" or "C violation". If both happens at the same event,
we evendently will speak of "CP Violation".
It's still not fully understood, but the "weak interaction" which as we know is involved in decay processes, exhibits "CP Violation",
which has been confirmed experimentally, for example by observing meson decays.
This is more strange than you might think at first sight. It effectively means that the mirror of the event shows a different decay
than the unmirrored version of the event. It's still puzzling up to this day, for example, why don't we see CP violations at the strong interaction?
This last sentence, is exactly why the (QCD) axion is postulated, and hunted for.
3.3.2. The "strong CP problem":
The "weak nuclear force", shows CP violations, as we simply see from experiments.
This force, is responsible, or is at work, with Beta decay. At the beginning of this section, we showed how a neutron
decayed into a proton, electron, and neutrino.
The "strong nuclear force", deals with how quarks "inside" a proton or neutron, interact, using gluons (a boson) and intricate
structures of the vacuum. "QCD" is the theory that tries to describe that.
But also larger atomic nuclei might show Beta decay. Some elements are not so "stable" as "others". You know that an atomic nucleus
is a collection of protons and neutrons. There is a sort of "optimal" number of protons and neutrons, to make an element really stable.
What I mean is this: if there is a large surplus of protons, the atom is not stable, but the other way around holds too, so if there is
a larger number of neutrons, the atom is not stable too.
If you like, you might see it this way, that in this case, Nature uses the weak nuclear force to arrive to stable atoms.
But, if such a decay takes place, the strong nuclear force has "to deal" with this "new" situation. You might see it, as if
the weak force now provided the input for the strong nuclear force.
There seems to be a real problem in this situation. It is expected that CP violation, with the strong nuclear force, would be observable too,
but that does not seem to be true. Simply put: experiments do not indicate any CP violation.
Hence the term: the "strong CP problem".
I am not sure if you would buy the story above. I think it's quite reasonable.
However, you can go to a physicist, and ask him/her to write down the most general equation that describes the "state" of the system (quarks, gluons, vacuum).
This then is a lengthy equation, and it would also include an "vacuum angle" θ which would represent the amount of CP violation.
As it turns out, when solutions are tested, θ is extremely small, or likely to be just "0".
Again, we have something missing, and it can be solved by a hypothetical particle, the axion, where axions are very light,
very weakly coupled to Standard Model matter (dark) and very long-lived.
Some say it has some features that make it resembles like a sort of "Higgs" scalar field.
So, as from, say 2006, the axion ball really got rolling, and many say that this is a good "dark matter" candidate.
Note:
Although the axion seems promising, other research on other types of WIMPs is still going on.
I don't want to give the impression that everybody have placed their bets on the axion: the search for other candidates still goes on.
In 2014, and beyond, experimental setups are in progress with the goal to detect the axion. It's likely that within a few years or so,
it can be decided if the axion really is what we are looking for.
You might also take a look at the links below.
Some nice articles about the QCD axion:
Axion Particle Dark Matter (npl.washington.edu) (large ppt file)
Axions from the Sun detected? (theguardian.com)
Axion (wikipedia)
ADMX (Axion Dark Matter Experiment) (phys.washington.edu)
Some tough articles about the QCD axion:
The Strong CP Problem and Axions (arxiv.org) (R. D. Peccei, one of the originators of Axions)
3.4 The Neutralino: another (but less likely) Dark Matter candidate in the "Traditional" Universe model.
I almost forgot to mention the "neutralino". However, presently the scientific community does not view it anymore as a good
candidate for "Dark Matter". But who knows? Maybe that will be revived at a later time.
However, a few folks still see some possibilities for neutralino forming during the early phases in the Universe. See chapter 4.
Let's first talk about fermions and bosons with respect to their spin, and the "Pauli excusion principle".
I should have put this in section 3.1.1, but let's put it here then.
What we have seen in section 3.1.1 is nice (I hope), but there is another difference between fermions and bosons.
It's their possible "spin" values, and the consequences thereof.
A fermion is (defined as) any particle that has an odd half-integer spin (like 1/2, 3/2, and so forth), so, our Quarks and leptons
have an half-integer spin. Quarks and leptons are the fundamental (elementary) particles, which we cannot (as the standard model says up to now),
decompose in even more fundamental particles.
However, even non-elementary particles may have an half-integer spin, so (according to the definition) they are fermions as well, like
for example the proton. But remember, these are not elementary particles (the quarks and leptons are).
Now, a similar story about Bosons. But remember, we have 6 "true" bosons (as listed in fig. 4) which are the force carriers (!).
I have to come to this part, otherwise it will be "hard" to go to the "neutralino" concept.
Bosons have an integer spin (like 0,1).
Likewise, a lot of other composite particles may also have an integer spin (like 0,1), and thus they classify as being a "boson" too.
As an extreme example: in a metallic lattice, two electrons (leptons) may "pair" up, in a certain extraordinary case, by which they
collectively have spin 0, and that pair then acts as a boson. Ok, maybe it sounds strange, because we usually only associate bosons with "force carriers".
As another example: a composite particle, like a 4He atom, always has spin 0, so it's a boson too (according to definition).
Now, the following is very remarkable (and fundamental):
- Fermions obey the Pauli Exclusion Principle and therefore cannot co-exist in the same state at same location at the same time.
Only one fermion can occupy a particular quantum state at any given time.
- Bosons can occupy the same quantum state. They can occupy the "same place" in space, with the same quantum properties.
The wave functions are symmetric under particle interchange, and they are allowed to be in the same state.
In "supersymmetry" it was proposed (or assumed) that all fermions and bosons, had an associated "superpartner", where only the spin differs by a half-integer.
But further, all other properties were the same (like mass, charge etc..).
You already see it happening? Suppose fermions have a "superpartner" where the "excusion principle" do not apply to.
In principle, it could lead to composites with a large mass and in where the charge could be 0 too, therefore it would make them "quite dark".
Alright, the full "supersymmetry" theories (not Superstring, but "supersymmetry") are more complicated than what's written above.
But, I hope you got the picture.
The "neutralino" then, would be such a "superpartner". Actually, theory would lead to a set four neutralino's, which are fermions with an integer spin.
The neutralino's, as the theory predicts, would only interact with the weak force bosons, and thus are "very dark", and thus difficult to detect.
But they have "mass" and thus could have accounted for "Dark Matter".
But any "superpartner" was never found, not even at LHC experiments, so, enthousiasm has significantly lowered in the scientific community.
However, in section 4.2 I will return to the hypothetical "neutralino" (as well as the "axion" from section 3.3).
The early Universe might have had some surprises for us...
Conclusions up to now (Chapters 1 & 2 & 3):
Chapters 1 & 2: As shown sofar, especially in section 2.3, Brane World scenario's have a true potential
of providing "dark matter" candidates, like the "branon".
Chapter 3: A traditional (single) Universe model, using Standard Model physics (particles, forces, bosons etc..),
have produced a real world "dark matter" candidates, most notably "the axion".
Chapter 4. Dark Matter and Inflationary Theories.
Personally, I like "Brane World" scenario's a lot. They are also used to explain the origin of (the) Universe(s).
And we have seen that they provide for "dark matter" candidates, but they even can be used to help explain "dark energy".
However, if you ask physicists and cosmologists about their thoughts on the "best" Theory (of the start) of the Universe which exists today,
it's likely that most will say: The Inflationary Universe theory.
And "indicators" that Inflation might be "the theory", is coming in... For example, remember the discovered "rippels" (B-mode polarization) in SpaceTime
from the BICEP2 data? If not, you might google on BICEP2 and inflation. If you are new to it: this will amaze you!
So, Inflation is quite unavoidable in discussing "dark matter" (and "dark energy").
Presently, you might say that "dark energy" is a condition that tries to rip space apart, or at least, accelerates it's expansion.
Strangely, it is suspected that "dark energy" gained true momentum at about 5 billion years ago. That's not fully established as a fact, but it is the current view.
However, logically, "dark matter" will try to lower the rate of expansion, since we have got a lot extra mass and gravitation in the Universe.
But that does not seem to happen. Well, "dark energy" is estimated to account for more than 68% of the total mass-energy in our observable Universe.
Dark Matter would than take up about 27%, leaving what's left, about 5%, for "normal" Standard Model matter.
From that perspective, it might be not so strange that dark energy will outwin gravitational pull.
4.1 Short introduction on Inflation.
A "Big Bang" that happened in space, is a wrong picture. In "Inflation", SpaceTime itself, was created in an "exponential" rate, during an amazingly
short period: the inflationary epoch.
In such a extremely small timeframe, like from 10-37 up to 10-32 second (indeed, incredably short), SpaceTime "suddenly" inflated by a factor
(which is often) estimated to be somewhere in the range of 1040 - 10100.
Many cosmologists say that an extremely short period precedes the inflationary epoch. This is often called the Planck era, from about 10-43 second
up to where "inflation" starts (10-37 sec). The very start, might be a form of a quantum fluctuation, but details are simply not clear.
This pre-inflationary state is seen by some as a "Quantum-Gravity" era where quantum events and pre-gravity were shortly "united".
It's important to note the "essence" of the inflationary epoch. This is how Alan Guth (one of the originators) describes the inflationary epoch:
At inflation, an initially extremely small region was under the influence of a repulsive, positive, gravitational effect, that pushes the region into exponential expansion.
The energy density remained constant, so during inflation, the total energy of SpaceTime increases an enormous factor like 1040 or much more.
This abnormal increase is however compensated, because of the field of the precursor of Gravity becomes more and more negative to compensate.
Remember that in Einsteins GRT, gravity is intrincally bound in SpaceTime geometry. So, such a balance is not a problem in physics.
During the inflationary epoch (the exponential expansion), you might see it this way, that a "field" existed, (or inflaton quanta), and acted as "gravitational repulsion"
thereby creating SpaceTime. From blackhole theories, you might know that normal gravity can be extremely strong, and might alter SpaceTime completely.
Our negative precursor of gravity, in this case, created SpaceTime. From Einsteins GRT theory, you probably know that gravity is geometrically bound to SpaceTime, so
that could help visualise why, in this case, SpaceTime was created.
It's not expected by most physicists and cosmologists that the Theory is "perfect" to explain every possible detail, however, as a general "framework",
it's quite successful, and some true indicators (from observations) have supported it's validity (e.g. BICEP2 data).
A large advantage of this way of approach, is that we have a remedy against the "horizon problem". Presently, if the background radiation is measured
in all directions, a map can be constructed which is highly "homogeneous". A sudden infation could account for such homogeneous background.
If you want to "visualise" that, there was no time to form "lumps" or other "in-homogeneous" structures (of whatever kind) at all.
However, it is believed that small, but significant, inhomogeneities remained, which are the tiny quantum fluctuations in the inflaton field itself.
This might have been the seed for Galaxy formation at much later stages.
Another important fact is, that observations seems to suggest that space is actually genuine ("euclidean") flat, and not "curved" (on a global scale),
as was often assumed a couple of decades ago. This is indeed predicted by most Inflationary theory variants.
Further, it is often assumed that Inflation ended at about 10-35, followed by a number of phases. Actually, most Inflationary variants are pretty complex in those phases.
Here are some "milestones":
Short after the true inflationary epoch, SpaceTime was actually synonymous to an instable False Vacuum, with a higher Energetic Potential than a true Vacuum.
It's a intrinsically unstable situation. At that moment, the Universe was still extremely hot. The potential of the false vacuum "rolled further down" and may be seen as a period
of particle creation (quark and lepton epoch), and symmetry breaking, where the different fundamental forces came to existence.
In the "Quark Epoch", estimated to be from 10-12 up to 10-6 seconds, probably first stated with a Quark Gluon Plasma.
Somewhat later, free quarks, electrons and neutrinos form in large numbers as the universe cools furher down to below 10 quadrillion degrees,
and the four fundamental forces assume their present forms.
As we also saw in section 3.3.1, quarks and antiquarks annihilate each other upon contact, but, in a process known as baryogenesis, a surplus of quarks
remain (due to a bias in the weak nuclear force), which will ultimately combine to form matter.
Then, a short period of creation of protons, neutrons followed, until the temperature dropped so far, that nuclei could be formed.
It's not advisable to take the listed "times" too strict. There is "some" small deviation between different arcticles.
When the Universe cooled down further, then at about 380000 years of age, the temperature was low enough for recombination to take place,
and electrons plus nuclei formed "atoms" (primarily Hydrogen and a small number of other light elements).
This made the Universe rather sudden "transparant" for light, and the first light could "travel" unhindered, without full scattering due to elementary particles,
like free electrons and other particles.
Note: many articles differentiate between a Planck era, GUT era etc.. Here, we have focussed on Inflation itself, and the epochs after that.
Fig 5. High-level view of the creation/evolution of the Universe.
Hopefully, this section provided for an understanding of the central ideas behind cosmic Inflation. Guth and Linde, both developed it at around 1980.
Since then, many variants have appeared. There even exists versions rewritten in the "Dark Energy" phenomenon.
Also, many articles have been published with very detailed studies on various particle creation physics, during, and shortly after, the Inflationary epoch.
That shows how lively it is in the scientific community.
4.2 Inflation and some ideas on Dark Matter.
In preparation: a number of relevant publications are under study now. I come back here.
At least, sofar, we have the following observations:
Observations sofar: (Chapters 1 & 2 & 3):
Chapters 1 & 2: As shown, especially in section 2.3, Brane World scenario's have a true potential
of providing "dark matter" candidates, like the "branon".
Chapter 3: A traditional (single) Universe model, using Standard Model physics (particles, forces, bosons etc..),
have produced a real world "dark matter" candidates, most notably "the axion".
Some other candidates are in consideration too, like supersymmetrical particles (e.g. neutralino).
Remark:
Hope you liked it sofar !
Ofcourse, every note that I produce, is free for use anyway you like it.