A few simple words on “Dark Energy” and some cosmological idea's.

Version : 1.2 – revised text.
Date : 22/06/2010
By : Albert van der Sel
Type of doc : just an attempt to decribe the subject in a few simple words. I am not sure if it's going to be any good.
For who : Introductionary note, so, it's for people who are not too familiar with the subjects

Contents:
1. Introduction.
2. Hubble and the expansion.
3. A few notes on the problems with the (original) Big Bang theory.
4. Large Scale Structure of the Universe (superclusters and voids).
5. The Inflationary Universe theory.
6. Dark Energy.
7. The Ekpyrotic Universe, or Brane World Cosmology.
8. Multiverse

1. Introduction.

Up to about 10 years ago, most cosmologists seemed to believe that the Universe expanded allright, but at a decelerating rate.

A few experimental groups set out to study a certain type of Supernova, to find more evidence to support the upper theorem.
What they instead have found, are clues (or evidence) that the Universe indeed decelerated to up to
5 billion years ago (5 Giga years - 5 Gy), and then, mysteriously, seemed to have picked up an acceleration again !

If you would just look at the total mass in the Universe, it would provide for a (pulling) gravitational effect.
But if the mass is too low, the Universe would expand, but probably at an ever decelerating rate.
If the mass would be high enough, the expansion would stop, and the Universe would eventually collapse
into the "Big Crunch".

If the observed acceleration is really true, then "something" must exert a negative pressure, outwinning the gravitational pull.
This 'something" is called "Dark Energy", and what it might be, is still unknown, altough a few "candidates" exists.

It must be said at this point, that not every scientist is convinced of either the concept of "Dark Energy", or
even the interpretation of the experimental data.
They form a minority, but some suggest that the equations of (for example) General Relativity, do not "apply that well" at large scales,
and should be revised. A few others say that the data should be corrected for certain effects (like galactic dust and stuff like that).
But.. the mainstream of scientists really think that "something" is going on, and that "Dark Energy" really manifests itself.

What could it then be?
It could even be "an old friend", like the vacuum itself, which in this context is synonym to the "Cosmological Constant".
The energy stored in the vacuum, then ultimately provides for the pressure.

But, in the context of string theories and hidden (extremely small) dimensions, some argue that
the dynamics of the hidden dimensions may play a role in the effect.

As another candidate (but maybe related in some way to the candidates above), a strange time depended field
called "quintessence", allways did exerted a certain small effect, but as time progressed, it suddenly picked up momentum,
just as if a sort of "sleeping" "spring" (in the vacuum) at some point thought is was now (5 Gy ago) about time to
to decompress "much harder" in some way.

In this small note, I would like to present a very simplified overview on the subject.
Ofcourse, many excellent documents can be found on the Internet, and mine is not a match at all.
So, please take a look at this document, but be warned (!) that really much better docs exists elsewhere.

The most important remark is this: don't believe anything "just like that". That holds ofcourse for "ad hoc" documents, of some "Albert",
(like this note), but also for scientific documents and presentations.
Fact is, we still don't know exactly what is going on, and there just is a certain amount of speculation around.

2. Hubble and the expansion.


Already in 1929, Hubble discovered that the further away an object (like a galaxy) was, the more "redshift" in the
frequency (of spectral lines) could be observed. This implied that the greater the distance was, the more "streched" the lightwaves are.
This phenomenon is attributed to the expansion of space itself !
In some books, you might have read, that galaxies further away, flee faster from us. This is not neccesarilly implied
by the redshift. What is likely to be true, is that the light has travelled through more and more streched space,
and thus gets more and more redshifted.
Now please note this remark: People often visualize the expansion of the Universe, as a sort of sphere that expands,
(or gets bigger and bigger), in the "Nothingness". That vision is not entirely ok. Take a look a the figure on the left.
Here, you see the surface of a balloon where dots are placed on the surface. If we inflate the balloon, the distance
between the dots increase. Actually, space itself inflates, just like the rubber surface of the balloon in the picture.

So, any observer in any galaxy, would see that the other galaxies (on a larger scale) flee away from them.

Now, that's a 2 Dimensional analog of the 4 Dimensional space-time Universe we live in. Really, the surface of the balloon
is a 2D curved "sheet". If you would like to visualize the expansion of the Universe, just "think away" the surroundings
of the balloon, and make mental transition of 2D to 4D (which is quite impossible to do ;-).

Even from the observed expansion alone, it is very tempting to speculate on a common Origin, and thus a "Big Bang" scenario
is stronly suggested. In 1948, George Gamow and Ralph Alpher formulated a (hot) Big Bang theory.
(Remarks: We should not forget the idea of the "primordeal" atom of Lemaitre in 1931.
Also, Alexander Friedmann already proposed in 1922, that the Universe might be expanding.
The remarkable findings of de Sitter around 1920, will also be touched in section 8).

3. A few notes on the problems with the (original) Big Bang theory.


If you would "wind back" time, and see all matter lumped together into a singularity, you get the hell
of a "nasty", incredible dense, and incredible hot "point". Still, this is what the original theory tells us.
What is truly spectecular, are the collaries of the theory. For example, the 3K background radition is correctly
predicted by the theory, as well as for example the ratio's of light elements in the Universe.

By now, there is remarkable precise "chart" of the biography (a curriculum vitae so to speak), that ranges
from various fractions of the first second of the "bang", to the first couple of minutes, up to couple of hunderds of thousends of years, up to the present age of about 13.7 billion years. This is depicted in the leftside figure.

But there are problems with the original model.
This document is ofcourse no indepth treatment of the Big Bang, but the most prominent problems were:
- horizon problem
- flatness problem
- a singularity is not in accordance with (for example) Quantum Theories

--> One of the Philosophical problems:
And ofcourse, we as Humans have (philosophical) difficulties with a Big Bang. For example, the question:
What was there before the Big Bang ? is a very legitimate question

To alleviate that philosophical problem, it helps if you realize, that time itself was "spatial" too.
What that "more or less" means, is that time is of the same dimensional "form" as a metric of distance.
So, if you can imagine a zero distance (that starts to grow), then the same is true for time.
This 'somewhat" implies, that if you have no problem with x = 0, then why bother with
"t =0 = no time" before the Big Bang?
Ofcourse, that is not fully satisfactionary, but may help a bit.
--> A few of The scientific problems:

- Flatness of space:

Space is likely to be flat. That is astounding to most folks, because years ago,
the notion lived amongst many, that the Universe was somehow a closed manifold in the sense that if you would
emit a ray of light, and waited billions of years, it would return to the same point again.
That does not hold anymore according to the most recent insights.
Locally, space is curved and distorted, since it's proven that light that passes massive objects
bends a little. But on the large scale, space seems to be flat (!)
For many (like me) this is hard to understand.

- Horizon problem:

Given the enormous size of the Universe, it is legitimate to speak of "causal disconnected regions".
Regions that are seperated by billions of lightyears, will not (immediately) interact.
Then why does the Universe seems to be so homogenic? Well, this has relaxed somewhat in modern views,
because so very "homogenic" is the Universe no more. But originally, for example, the homegeneous 3K radiaton
puzzled a lot of people. This is related to the "horizon problem".
This, and other considerations, led to a "revision" of the Big Bang.
This revision is called the "Inflationary Universe" theory.

4. Large Scale Structure of the Universe.


It's probably known to you, that the "Large Scale Structure" of distribution of galaxies (like our milkyway),
is not like a smooth uniform distribution of galaxies. On the contrary ! Galaxies seems to be clustered, while those
clusters are part of "superclusters", with "voids" and "supervoids" in between !
The figure on the left tries to illustrate that. This is ofcourse very puzzling.
If you take as a sort of "average" that the size of a galaxy is about 100.000 lightyears (about the size of our galaxy),
you can compare that to the fact that a superclusters can span, say, a hundred millions of light-years.
What is so typical, is that a supercluster resembles a 1D filament, a sort of string, or tube like form, of galaxies.
This results in a sort "lattice" structure, or if you like, a sort of "swiss cheese" structure, with many "holes".
How is that possible? And what exists in the "voids"?
Many cosmologists think that the "voids" contain something that's called "Dark Matter", but that debate is far
from over !

COBE, and later WMAP, showed tiny variations in the temperature "distribution of the 3K background radiation, due
to the Big Bang. WMAP resulted in a sort of precise temperature "map", of the Universe, as it existed about 400.000 years
after the Bang. Here, it is very tempting to speculate, that those tiny variations, is somehow related to the current swiss-cheese
structure of our Universe. At the time that "ordinary" matter came to existence, the tiny variations might have
favoured gravity to lump the matter into pre-galaxy types of structures.
Indeed, that seems to be the consensus with many cosmologists today.
Ofcourse, other questions arose, like what caused those variations?
Again, multiple explanations exists like "Topological defects", and "Inflation".
The measured values of WMAP seems to support the "Inflationary" model, so now it's about time to spend
a few words on the "Inflationary Universe" model.

5. The Inflationary Universe theory.


Horizon problem:
If you would take a look again at the WMAP figure, of the cosmic microwave background (CMB), you see the
tiny variations in temperature. But, WMAP is very precise! In fact, the differences in intensities is no more
than 1 part in 100000. This relates to the horizon problem. If you would assume a normal Big Bang, anomalies in the
pattern were certainly bound to arise. This is natural, because interactions between regions would take too much time
(so to speak). Regions would be out of each other horizons, too smooth out the differences in temperature.
It's the puzzle that the Universe looks the "same" on opposite sides of the sky (opposite horizons) right now,
as is shown by WMAP.
So how do the opposite horizons "know" how to keep in step (or so smooth in intensity) with each other?
The Horizon problem points us to the fact that different regions of the universe have not "contacted" each other
due to the great distances between them, but nevertheless they have the same temperature and other physical properties.
Keypoint is thus, that the uniformity of the cosmic microwave background temperature, actually tells us that these regions
must have been in contact with each other in the past. Still, this fingerprint is observable today, and determines
this characteristic backround radiation througout the entire (observable) Universe.

Inflation:
The idea that Alan Guth developed in his "Inflationary Universe" theory, essentially uses a quantum fluctuation, producing
a false vacuum in an extremely tiny "area" (which actually might not be called "space", as we think of it today).
The remarkable thing of the false vacuum, stem from its pressure, which is large and negative.
. Now, in general relativity, pressure has a gravitational effect similar to that of energy and mass, and while positive pressure
causes gravitational attraction and thus decelerates any expansion, negative pressure
(really!) causes gravitational repulsion and thus accelerates the expansion of the universe.
The theory further implies an exponential expansion, causing to unfold a more "true vacuum" or space
in a tremendous rate. This extremely short period is called "the inflationary epoch" of the Big Bang
At a certain time (this is not exactly known), the energy of the false vacuum decays into particles (or strings),
and the inflationary epoch is over and is continued by the classical Big bang theory.

I agree that this is still somewhat vague. In an analogy used by Guth himself, imagine a piston.
Inside the piston, exists a false vacuum, with energy and a negative pressure. Gravitation pushes, or if you want,
the negative pressure, "sucks in" the piston, creating real space as the piston "moves in".
Now, do not project this in such way that the false vacuum gets smaller. The above analogy is just an analogy,
and it has it flaws.

Whatever existed in the inflationary epoch, like matter and energy, it all "ride along" with this explosive expansion of space
preserving their properties. This then should explain why the CMB shows such a remarkable uniformity.

The inflationary theory does not make assumptions on where exactly inflation "stops", which might be perceived
as a weak point.
The flatness problem:
As I warned you, to beware of any "adhoc" documents (like mine), I doubted a bit, if I would include
this subsection. Anyway, at this point I say "why not"?.

In the figure on the left, you might see why our observable universe seems flat.
The various circles represent the "size" of the universe during the inflationary period.
But.. lhe largest circle, represent our Universe as it is "today", while the observable universe is
represented by the red line. That red line, is "flat space" as perceived by us.
From inflation alone, we cannot deduce that the "whole universe" is flat as well.
Only "as far as we can see", it all looks flat.
Now, it's likely that all space is flat, but this section deals with inflation, and the figure on the left
tries to illustrate how inflation resolved the flatness problem.
So, from inflation alone, there is no garantee, that the Universe is really flat.
Only, just like on earth, when looking at the horizon, the curvature is so streched,
so that it all "seems" flat.
But I included that only in the context of why inflation helps to solve problems.

The inflationary theory thus says nothing about the "true" size of the universe.
If you look at the figure on the left, the "real" universe is thus much larger than
we can observe today.
As another remarkable point, I would like to add this point. Suppose we take a look at the Universe, when it was, say,
1Gy old. The Big Bang is over. Now, the Universe expands, but certainly not at lightspeed.
In this case, light emitted from objects, have enough time to "wrap" around the Universe again (!),
if it was indeed a closed (curved) Universe.
If space would be closed, we would probably (?) see multiple "dots" representing the same object.
But even in our time, that phenomenon would manifest itself.
Now, this effect is not likely to have been observed at all. It's not present in WMAP as well.
So, it is a clue that the Universe is flat allright, or indeed the curvature is so large by now
(as illustrated in the above figure), that the effect cannot be seen due to the large size of the Universe.
Or, ofcourse, it is also possible that light cannot be "wrapped around", due to some reason. We just don't know.


But, there exists an interresting alternative for the Inflationary model and the Big Bang.
This wil be the subject of section 7.

6. Dark Energy.


The weird thing that seems to have been observed, is that the Universe gradually decelerated (but still expanded),
then, slowly, the expansion picked up "speed' again, resulting to the acceleration of the expansion,
as we can see today.
Why? How?
There are two reasonable candidates for Dark Energy: the (usual) "vacuum energy density" (or cosmological constant),
and something "new" which is called "quintessence"

Some cosmologists describe "quintessence" as a sort of "field that slept, awoke, and now drives the acceleration".
Also, for many cosmologists,"quintessence" is synonymous to "Dark Energy", making both concepts the same thing.

Why isn't it likely to be the "vacuum energy density"? The same cosmologist say that the problem with the cosmological constant,
is, that it is constant, with the same energy density, pressure, and equation of state over time.
The point they make is, that the stuff that's Dark energy, had to be "negligible" at the universe's earliest stages.
If not, the galaxies and all their stars etc.. would never have formed.
That is not a strange idea. If there was a strong negative "pressure" in the beginning, it's really hard
to see how galaxies could have formed.
So, quintessence" is viewed as a time and space varied field, that was using a "low profile" in the early Universe,
and "some" time ago (approximately 5Gy ago), got more and more prominent.

As a third, more traditional approach:
The normal energy and mass in the Universe will provide for a gravitational pull.
The energy in the vacuum (a scalar field, or the 'Dark Energy"), will exert a negative pressure.

As the universe expands, mass and energy "sort of" dillutes, so that a certain point in time, the effect
of the negative pressure (repulsive gravity), starts to outwin the normal gravitational pull.

So, according to this "model", in the early billion of years of the existence of the Universe,
the gravitational pull was the dominant effect, so that the expansion decelerated.
But the Universe growed. At a certain moment (so to speak) the negative pressure became "dominant".
In this scenario, the Universe will start to expand faster and faster.

The idea sketched above, have some appealing sides to it. But other explanations exist as well.
Now, the idea has a mathematical equivalent ofcourse. But just expressed in simple words, as I tried above,
it is a simple and elegant idea. At least, that's my opinion.
Before we go to alternatives of the negative pressure of the Vacuum, let's explore a "sort of alternative"
(or other description) of the inflationary and Big bang models.

7. The Ekpyrotic Universe, or Brane World Cosmology:


SF writers will never beat, what many scientists launches as viable theories.
Especially from the Superstring - M-Theory people, an interresting idea has been put forward, as a
mechanism that created the Universe (or I should say: our Universe).

To refresh your memory a bit, in string theories, "particles" are represented by vibrating strings. The different "harmonics"
of the strings, correspond to the different particles we see today.
Furthermore, string theories are based on extra dimensions and branes.
M-Theory now works with 11 dimensions. Strings may have put their 'eindpoints" on branes.

The "Ekpyrotic Universe" model, suggest that our Universe came into existence, after a collision
of two "branes". This collision released a large amount of energy which would appear very similar
to the classic big bang, but avoids the singularity.

Slightly different versions exists. One version states that two perfectly vacuous "branes" somehow
(by some interaction) slowly attracted each other, and finally collided, and produces a sort
of false vacuum again. This then, ulimately, results in our present Universe, with radiation and matter.
Interestingly, this particular "bubble" is then doomed to expand and gradually will decay into a perfect
vacuum again.
This scenario, suggests also an endless cycle of "Universe creations", that will all decay (slowly, like our own Universe)
into a vacuous Brane again.

It should be mentioned that this model addresses the flatness problem, as well as the horizon problem,
just like the inflationary model did.

As said before, this theory avoids the singularity (Big Bang) or quantum fluctuation (Inflation),
and thats why it is appealing to a number of cosmologists.

But what about "Dark Energy"? It's likely that we may apply the same principle again as we used in section 6.
The negative pressure will, at a certain point, "outwin" the gravitational pull.

In Brane Cosmology, other interpretations exists as well.
Instead of a decaying Universe, a cyclic Universe is proposed. Two branes collide, giving rise to a Universe.
The branes then still encompass that Universe.
After a period of acceleration, a deceleration begins, upto a contraction. Ultimately, the branes collide again,
which creates the Universe again etc.. etc..
Nice theory, but it does not fit in the observations as scientists have them now.

But, a keypoint here, is this particular field of research (Brane Cosmology) is very lively today,
and many cosmologists seem to favour the "brane solutions" over inflation.


8. The Multiverse:


Many ideas have been launced, describing different forms of "Multiverses"
They all describe the various universes within a Multiverse.
There are even "classification levels", which I will not discuss in this short note.
Below, you will only find just a few of those ideas.

There are many "suggestions" for having a sort of Multiverse:

=> It might be inferred from M-theory, that our universe and others are created by collisions
between p-branes. Each universe takes the form of a D-brane. Objects in each universe are essentially
confined to the D-brane of their universe, but may (or may not) be able to interact with other universes.
For example, gravity, or gravitons, which are closed strings not with their endfoots placed on D-branes,
may be able to leak away from their Universe.

That's really a facinating theory. Multiple 4 dimensional (time+3D) branes could exists, or in other words,
multiple independed Universes could thus exists, in a higher dimensional superspace (also called the "bulk").
Please see my second note for more information.

As for a totally different Multiverse interpretation:

=> The formation of a single universe as "bubble" in a multiverse, was proposed by A. Linde.
This Bubble universe theory arises from the "chaotic theory of inflation".
Some "parent" might provide for a condition (a fluctuation) that starts inflation.
"Somewhere else", at another parent, the same might happen. But due to different potentials,
the Universes could be very different, with other constants of nature and other laws of physics.
Some may have a relative long-term expansion, which allows matter and large-scale galactic structures to form.
So, for example, our Universe may be just one of the bubbles in the Multiverse.

As an interresting speculation: the Antropic principle might be applied.
Since there are so many possible Universes, with their own physics, only a few (or maybe one?)
might be "finetuned" enough, so that galaxies may form.. planets may form.., and may support life
as we know it.

The "CMB cold spot" is quite intruiging. Maybe you yourself like to search the Internet
what that "cold spot" could mean.

For now, I conclude this simple note. As always, whatever I write (and have put on the site) is free.
Nobody needs permission to copy whatever from my stuff, or need to ask.

Maybe it can even serve as inspiration for some school project for a kid?


Hope you have liked it !