<html>
<body>

<h1>A few words on DE, Branes, Expansion of the Universe, and "stuff".</h1>

<B>Version</B>	    : 0.7.<br>
<B>Date</B>		: 24/06/2010<br>
<B>By</B>		    : Albert van der Sel<br>
<B>Type of doc</B>	: This is my note. It's Just a few speculations. But... hopefully you like them.<br>

<hr/>
<br>
You might know, that the latest insights tells us, that the Universe is expanding at an <I>increasing</I> rate.<br>
What's really weird is, that (since the Big Bang) the Universe expanded, but gradually slowed down in the rate, due to gravity.<br>
Then, for whatever reason, the acceleration seemed picked up momentum again. And that's the weird part.<br>
<br>
<I>Note: the effect is likely to be real, but is still questioned by a number of scientists.</I><br>
<br>
As it looks now, the Universe will expand faster and faster, until there's nothing left anymore, <br>
as if the vacuum will fully decay "into something" we don't exactly know about.<br>
There are idea's allright in the scientific community. Like for example "Dark Energy" (DE) which is supposed to exert<br>
a "negative" pressure, which counteracts gravity.<br>
DE is believed to be about 70% of the total energy of the present Universe. This then, causes the expansion<br>
of the Universe to accelerate.<br> 
<br>
Now, to what DE actually <I>is</I>, some argue, that it is just the "vacuum energy density". They say that wo do not need<br>
to look further for some other exotic field.<br>
<br>
Still, some others say that the "vacuum energy density" is (globally) "constant" and see that as problematic for the acceleration.<br>
They then postulate an additional sort of space-time varying field, that recently went 'stronger' and now drives the acceleration.<br>
<br>
Still another, <I>but probably wrong</I>, easy viewpoint could be this:<br>
Dark Energy could possibly be some unknown field, that always has exerted a certain pressure.<br>
Now, since the matter (sort of) dilutes with the expansion, we can imagin that at some point, the Dark Energy <br>
starts to "outwin" gravity, resulting in faster and faster expansion.<br>
It's just like some "imbalance" starts to occur at some point: as the total of matter expands, that is, sort of dillutes,<br>
the gravitation gradually gets "weaker" and weaker.<br> 
Then, the negative pressure gets relatively stronger and stronger, compared to the gravity, and thus acceleration is unavoidable.<br>
But as said before, this is not accepted much by scientists, and most of them "bet their horses" on some strange field<br>
that long ago was weak, and got stronger, which effect is somehow related to space and time.<br>
<br>
Also, but not often heard, are viewpoints that relate a 3 brane with closed strings, as regular particles with<br>
a number of know forces (like electromagnetic, nuclear, weak force) <I> on the one side</I>, and closed strings<br>
like gravitons, <I>on the other side</I>, wich are able to leak away into the higher dimensional superspace.<br>
This then, could contribute to the effects we observe in our Universe (our brane).<br>
<br>
There are many viewpoints that "more or less" relate to the above.<br>
Below are just a few considerations, (but be warned: they could be totally wrong...!)<br>
<br>
Remark: it's perhaps best to read the note <I>"1.1 Short simplified Overview on DE and the acceleration of the Universe"</I>, first.<br>

<br>
<H2>Note 1: gravitons escaping our D brane.</H2>

Superstring theory predicts the existence of new objects, called p-branes (where p is the number of spatial dimensions they occupy)<br>
Certain p-branes are called D-branes. They have the property that strings can end on them.<br>
It's tempting to view the observable Universe as a 3-brane, which is embedded in a space with 6 additional spatial dimensions (the bulk)<br>.
So, our "standard particles" (photons, quarks and leptons), exist only in three-dimensional subspace: the three-brane.<br>
But there are also those hidden (extra) dimensions, which is known, as said before, as "the bulk".<br> 
<br>
Note: The idea that the universe (that is particles) is trapped on a membrane ("brane") in some high-dimensional space-time,<br>
might even explain why gravity is so weak, compared to other forces.<br>
<br>

<img src="de11.jpg" align="left"/>
Actually, the theory permits <I>sets</I> of three-branes, resulting in multiple independent Universes.<br>
<br>
Each universe takes the form of a D-brane. Objects in each universe are essentially<br>
confined to the D-brane of their universe, but may (or may not) be able to interact with other universes.<br>
For example, gravity, or gravitons, which are closed strings, not with their endfoots placed on D-branes,<br>
may be able to leak away from their Universe.<br>
<br>
In the figure on the left, you see the regular particles which are bound on their three-brane,
while the gravitons (which are closed strings) are not, and are probably able to vanish from the Universe.<br>
<br>
Some theorist even goes that far as saying that gravity actually is, (or wants to), "living in the bulk", meaning that
it's more natural for gravitons to leak from our 3-brane to the bulk.<br>
<br>
It's not impossible that large accelerator experiments, will show that a collision (e.g. of a proton and anti-proton),
will produce (among other familiar particles), a graviton, which might escapes to the bulk.
We, on the 3 brane, might then observe an imbalance in energy, which supports the upper theory.<br>
<br>
So, if this scenario is really true, why does one need Dark Energy to explain the acceleration of the Universe?<br>
Since gravitons "like to flee away" to the bulk anyway, then overall gravity in/on our Brane lowers, <B>so.. there you are!</B><br>
Well, that exlanation is, to some degree, doubtfull and really <I>to easy</I>.<br>
Some folks argue in the following way:<br>
Forces like electromagnetism and the nuclear force, only operate in our 3 spatial dimensions, that is, in the 3-brane,<br>
while gravity <B>operates</B> in <B>all</B> spatial 10 dimensions, so out of the 3 brane as well.<br>
<br>
For now, I think we can conclude that "escaping gravitons" is likely no alternative for Dark Energy.<br>
Or is it? Anyway, most scientists don't believe that.<br>
So, in the next sections, more "accepted" models will be discused.<br>
<br>
Note: the following is <I>very</I> speculative: As the Universe expanded, there became more and more "room" or "opportunity"<br>
for gravitons to escape from our "M brane". It all just simply became larger, and simpler to escape to the bulk.<br>
It's a self-enhancing effect ! Could that then be a consideration? (I don't know)<br>
<br>

<H2>Note 2: The "vacuum energy density", and "quintessence"</H2>

<h3>2.1 Introduction.</h3>
There are two reasonable candidates for Dark Energy: the (usual) "vacuum energy density" (or cosmological constant),<br>
and something "new" which is called "quintessence".<br>
As a third option, the facinating "Brane Cosmology" should be mentioned. This is the subject of section 3.<br>
Let's first take a look at the first two "candidates".<br>
<br>
Some cosmologists describe "quintessence" as a sort of <I>"field that slept, awoke, and now drives the acceleration"</I>.<br>
Also, for many cosmologists,"quintessence" is synonymous to "Dark Energy", making both concepts the same thing.<br> 
<br>
Why can't it just be the "vacuum energy density"? The same cosmologist say that the problem with the cosmological constant,<br>
is, that it is <B><I>constant</B></I>, with the same energy density, pressure, and equation of state over time.<br>
The point they make is, that the stuff that's Dark energy, had to be "negligible" at the universe's earliest stages.<br>
If not, the galaxies and all their stars etc.. would never have formed.<br>
That is not a strange idea. If there was a strong negative "pressure" in the beginning, it's really hard<br>
to see how galaxies could have formed.<br>
<br>
So, there are advocates who favor the "ordinary" vacuum energy density (or, equivalently, the cosmological constant)<br>
and, on the other hand, advocates who favor "quintessence", which is supposed to be a time-evolving, spatially inhomogeneous<br>
component exerting negative pressure.
<br>
<h3>2.2 The (ordinary) vacuum energy density</h3>
The "cosmological constant" was first introduced by Einstein. His "Theory of General Relativity", implied that<br>
the Universe would collapse, due to gravitational effects.<br>
At that time however, it was believed that the Universe was 'static', so for the purpose of constructing a static model<br>
of the universe, Einstein added the Cosmological Constant. This (repulsive) cosmological constant should then balance<br>
the gravitational attraction of matter. Today, the cosmological constant is by many scientists recognized as vacuum energy,<br>
an energy assigned to empty space itself, that has negative pressure and induces cosmic acceleration (!)<br>
<br>
So, the Cosmological Constant really may be associated with negative pressure and accelerated expansion(!)<br>
<br>
In my notes, you will not find mutch math. But the following nice example, will demonstrate why the <B>vacuum energy</B><br>
relates to <B>accelerated expansion</B> "of space", or "the vacuum".</B><br>
<br>
Needless to say that Einsteins General Relativity (GR) equations are pretty tough.<br>
The Friedmann–Lemaître–Robertson–Walker (FLRW) metric is an certain solution of Einstein's field equations of GR.<br>
It uses certain asumptions, like a homogeneous, isotropic Universe. Many scientists regard it to be at least a usable<br>
first order approcimation. Below you see some of the results:<br>

<img src="de14.jpg" align="left" />  
<br>
In second equation, if you look at the first term on the right of the "=", actually tells us that both the energy density<br>
and the pressure cause the expansion rate of the universe to decrease, as a consequence of gravitation.<br>
But (!) the second part on the right, thus cosmological constant Λ, on the other hand, causes an <B>acceleration</B><br>
in the expansion of the universe.<br>
<br>
<br>
To put it simple: the equation says that the rate of acceleration (a), is a "negative part" plus a "positive part", which is<br>
equivalent to saying "attraction due to gravity" plus "repulsion due to negative pressure of the vacuum".<br>
If the second term is larger than the first term, we then have a positive rate of acceleration (!)<br>
<br>
This is why some scientists concentrate on the cosmological constant. But as said before, the fact that it is regarded<br>
as a "constant", does not explain why the repulsion in the very early Universe must have been low, that is, low enough<br>
for galaxies to form.<br>
By the way, not all scientists are really convinced the cosmological constant, was trully constant all the time. But, that's all<br>
quite speculative at this time.<br>
<br>
And, some mathematical treatments show that even a constant Λ will give rise to an accelerated Universe, although<br>
it seems difficult to reconcile that with the early formation of galaxies.<br>
<br>
It's quite fair to say that we do not have a "very" clear picture right now.<br> 
<br>
<h3>2.3 Quintessence</h3>
What is a reasonable description of quintessence ? Is it the same, or part of, the vacuum energy?<br>
In fact, it is not easy to answer the last question.<br> 
Some arguments might be the following:<br>
<br>
1. the vacuum energy or Cosmological constant, is (supposedly) "constant" in space and time. This is likely not be so<br>
for quintessence. That field should be "low in magitude" at the early stages of the Universe, while at a later phase,<br>
it increased significantly: there must be a period in the early Universe where this force was negligible,<br>
otherwise galaxies and stars would probably not have formed.<br>
This, as many scientists assumes, sets quintessence "apart" from the Cosmological Constant.<br>
<br>
2. The vacuum energy, or "vacuum fluctuations", as is understood in small scale observations as for example,<br>
in the "Casimir effect", or the "Lamb" shift in spectral lines of Hydrogen (and other elements), is contributed<br>
to the virtual particles, or quantum fluctuations, in the local vacuum.<br>
This is likely not to be attributed to quintessence.<br>
<br>
3. Both the vacuum energy and quintessence, can be expressed by the "equation of state",<B> w ~ p/p' </B>where p<br>
is the pressure and p' is the is the energy density. For the vacuum, w is believed to be "-1".<br>
Different ideas on quintessence, produces a different "w".<br>
<br>
What seems to be characteristic for quintessence, is that it's scalar value is often viewed as a "slow rolling potential",<br>
<img src="de16.jpg" align="left" /> 
In the equation on the left, the wavelength should be very long, that is, a slow rolling potential with little<br>
kinetic energy and a larger potential part (second term on the leftside of the "=").<br> 
<br>
Simply put: in the equation above, you see on the right side of the "=", a postive term and a negative term.<br>
Now, if the kinetic energy is smaller (due to the slow roll) than the negative potential term, we have a a negative pressure. <br>
This then, implies an accelerated expansion.<br>
<br>
So what's best? Vacuum energy density or quintessence, or still something else? There are advocates for both models.<br>
But if you take a look at the number of publications on quintessence, or quintessence in combination with the<br>
"new" inflationary theory (a renewed theory from Guth's original one), it seems that "quintessence"<br>
is quite popular among scientists.<br>   
<br>
<br>
<br>
<br>
</body>
</html>�