A very simple note on "Colliding Branes (Brane World scenario's)".

Version : 0.2
Date : 5 May, 2014
By : Albert van der Sel
Type of doc : Just an attempt to decribe the subject in a few simple words. Hopefully, it's any good.


Several good theories exists, and are in permanent refinement, to explain the origin of the Universe.

Most cosmologists and physicist would vote for the "Inflationary Universe" model. Indeed, it provides solutions
for the "flatness problem", and the "Horizon problem", to name a few.
Another important theory (among other theories!) has a different "look and feel", namely "Colliding Branes", primarily arising from
Superstring theories.


1. First, a few words on Inflation:

Everbody knows of the "Big Bang", ofcourse. A refinement to this, with more detailed descriptions, is the "Inflationary" model.
The word "inflation" already gives a hint to what it means: a superfast inflation of space-time.

In simple words, Inflation is about this:

From (presumably) a quantum fluctuation, an exponentially rapid expansion of an unstable "space-time" state occurred.
Understand it this way, that "space-time" was created in an unbelievable short timeframe. This spacetime was in a
state of a "False vacuum".
The inflation was driven by a "negative pressure", which can be seen as a precursor to gravity.

Actually, the theory describes various phases, like phases of supercooling and re-heating. We skip all that. At a certain point, we have a situation
where the potential of the False Vacuum 'looks' like the form of a "Mexican hat", where the potential then "rolled down" from the top,
which gave rise to various fields (like Higgs) and particles. From that point on, then a more "*familiar*" Universe starts to form, with particles,
fields, and forces like we know them today.

It seems like a good theory. It also has a few amazing features, and solves a few theoretical problems.

One hard thing in physics is, how to reconsile Quantum mechanics with a theory of Gravity. Inflation gives us a small hint:
From the very first Quantum fluctuation at start, almost immediately positive gravity drives inflation and creates space/time.
This "sort of" seems to link them at extremely high temperatures or energy.

But what Inflation really seems to solve, is the flatness of spacetime and the Horizon problem.

In the observable Universe (as far as we can see), space looks "flat" or Eucledian. Except local bendings around massive objects,
at large scale, space is flat, in accordance with Inflationary theories.

The non-observable Universe is so large, that causally disconnected regions exists. Those regions have their own "Horizons".
Signals, even if speeding with "c", cannot reach other regions, simply because too much space, and continuously expanding space, exists.
When the Universe was still extremely small, following was the sudden "inflation" which conserved the properties of all space of that moment,
thereby making the Universe globally homogeneous.

All in all, the "Inflationary Theory" has a high degree of acceptance between cosmologists and physicists.


Now, this note tries to say something about a competing theory, which is: "Colliding Branes" - or - "The Ekpyrotic Universe".
So, let's do that then.


2. A few words on "Colliding Branes":

Actually, there is not "just one" Colliding Branes theory. Those men and woman in cosmology, or theoretical physics,
have such a high amount of creativity and knowledge, that many dozens of variants are "under construction", all the time.
Sometimes, they abondan a model, and often new promising idea emerges.
By the way, the same is true for Inflationary theories.

So, the only thing I like to do here (with a reasonable level of realism for such a short note) is just presenting some
of the very basic ideas behind it. And..., I am a simple mortal too..., with just a basic understanding...

The traditional Big Bang theory, and even Inflation..., might have a nasty start: it's the "Singularity".
Especially physicist, never seem to like "true zero" points. It's just that every equation breaks down at "0".

Question remains however, in how much Inflation truly speaks of an initial Singularity. It actually only sort of postulate
a Quantum fluctuation (of some sort) from a condition that had no spacetime as we know it today.

Another question might be this: WHY would there be a "quantum fluctuation" that is supposed to ignite the "Big Bang" or "Inflation" ?
Some might answer this by pointing to the intrinsic indeterminism, and probability based, character of QM.

Another route is the "Ekpyrotic Universe" theory. It makes use of concepts and ideas from superstring- and brane theories.

Note: If you want to get a quick intro in such ideas, you might take a look at this note.

The whole approach in the Ekpyrotic Universe is quite different from the origininal Inflationary Theory.

⇒ Early attempts, using string theories:

Actually, it was quite natural, that at some stage, people tried to use string theories to understand the origin of the Universe.
One of the first attempts also stems from the early 80s, short after the Inflational Theory. This idea postulated a string
of 9 compactified dimensions, with a metric in the order of the Planck scale. Using quite advanced mathematics (which unfortunately
is always the case in superstring theories), the authors showed that after a certain event, just 3 dimensions unfolded,
while the others stayed compactified, resulting in a Big Bang like scenario, and resulted in a Universe as we see it today.

However, it was shown shortly afterwards, that it was actually difficult to maintain exactly why just 3 space dimensions unfolded.
Although the theory was not entirely placed in the refrigerator, string theorists found better scenarios without obvious "flaws".

Besides all this, any alternative for Inflation should also give good clues on how to handle the flatness- and Horizon problems.
Better yet, if a theory provides for a handle to explain "Dark Matter" and "Dark Energy", then that would really be something !

⇒ Colliding Branes:

Superstring theories use 10 space-time dimensions, of which 3 are the usual spatial dimensions we know so well, and 6
spatial dimensions are compactified to a metric in the order of the Planck scale (and thus are so small, that they go practically undetectable).
Using a "rather difficult mathematics", and certain boundary conditions, the notion of a "Brane" emerged. It's generally speaking some
N-dimensional "manifold" which relate to strings (the elementary particles).

A "D brane" is a special case of branes, where the ends of "open strings" (=particles) are localized on. So, the usual elementary particles (the "strings")
are bound (or restricted) to "live" on the brane only.
If you want (and many people do), view such a manifold as for example our 4 dimensional spacetime (our Universe).

Fig 1. Open strings are bound on the Manifold. Closed strings are not.



Amazingly, "closed strings" like the "graviton", are not bound to that manifold. They are thus "free".
On the other hand, the particles which are open strings (quarks, electrons) are bound to the Brane.
So, in such a way of thinking, the force carrier (boson) of Gravity, the "graviton", is not bound to our Manifold.

Note: this kind of science is very active. Many theoretical physicists have published articles with severe modifications, or
refinements, to the "general" (or public/popular) view of superstring theories. It's sometimes looks like a sort of Formula-1 field,
where almost only insiders have a clue what the other guy is talking about...

Using a bit of fantasy, just view such a Brane, as a substructure (like a "plane") in some sort of higher dimensional "Hyperspace".

Now, what if multiple (infinite?) Primordial Branes exists, floating in some sort of Bulk space?
If gravity (or a precursor) interacts between Branes, they might "collide" or "intersect".
Such a collision, then avoids the "primordial singularity" and could be the origin of the Big Bang..

There actually exists quite a few models.

- One idea is that two (more or less) parallel branes, due to gravity, collided. Some models then say that an 4 dimensional
manifold is violently created, much like a "Big Bang" scenario. One obvious advantage is that the Singularity is absent.

- Another idea says that a Brane collided with "our Brane", which resulted in a tremendous Energy input,
which might explain why the Universe undergoes an accelerated expansion.
The (alien) matter from the second Brane then might be the "Dark Matter" which only interacts with "our" matter with gravity.
Such a model would then explain the existence of "Dark Matter" as it was originating from the second Brane.
So, actually, "Dark Matter" then just is the matter from the second brane (from our perspective).

⇒ One nice (grandfather) model:

The next model is actually pretty "old", but still is one of the "grandfathers" of newer models and ideas.

M-Theory is a unification of several superstring theories. It works with 10 spatial dimensions, and 1 time dimension,
so it's an 11 dim Theory. The basic "ingredients" are strings and Branes (as we saw above).
It was often assumed, that apart from the 3 "visible" spatial dimensions, the other spatial dimensions are compactified
to an immensly small scale (order of the Planck length 10-35 m).

However, some have argued that some of those dimensions do not a priori have be "so small".

Especially there exists considerations as to why a 5th dimension (the 4th spatial one) is "special".

In that case, you can express the full space/time "M11", as a product of

- spacetime as we know it (M4), with

- Z (the fifth dimension), with

- 6 compactified dimensions (sometimes called Calabi-Yau space Y6).

So, that can be expressed like:

M11= M4 (our space) x Z x Y6

In such scenario, "Z" (the fifth dimension) is larger than the compactified dimensions of the Calabi-Yau construct.

Now, in the model, M4 Branes can "move" along Z, and thus it's even possible that they Collide, or just are "close" to each other.

Fig 2. Close, or colliding Branes (move along Z).



Interesting ideas may follow. It's generally assumed, and quite fair to do so, that each Brane has it's own physical laws, constants,
and if matter is present, it's "own" type of matter as well.

Even if they are "just close", the free gravitons may interact with all matter, and thus an observer in one Brane, may even think that
strange "Dark matter" is around.

These are not speculations. They are serious ideas. However, "Inflation" is seen by many folks as the best we have up to today.

However, keep in mind that any Cosmological Theory should deal "somehow" with our new insights to "Dark Energy" and "Dark Matter".

Originally, a "cyclic" variant of the model with colliding Branes, is often viewed as the "The Ekpyrotic Universe" model.
But, sometimes a "one time" event goes under that same name as well.


Well, that's it. Maybe you liked it. You are strongly encouraged to Google further on "Colliding Branes".