Some Theories on Parallel Universes.

Date : 7 July, 2016
Version: 0.5
By: Albert van der Sel
Status: Still working.
Remark: Please refresh the page to see any updates.

Some theories from Physics on parallel universes.

Fig. 1: Here, 7 approaches are shown in simple pictorial figures.

It's true that at least 7 or 8 "ideas"/"models" exists, from which it follows that the existence of parallel universes
might be possible. Here, a few originate from "interpretations" of Quantum Mechanics, while some others have emerged
from theoretical physics and cosmological models.

Let's take a brief look what on they are about... Maybe you even like it!

One small thing though... and just for the record... there is nothing "hazy" here,
since they all are real ideas from Physics.
If you don't believe that, just Google on for example "Inflation Multiverse" or "Everett MWI", or "Poirier parallel universe"
or "brane cosmology" etc..
It's even better if you add "arxiv" as a search term, since that will list mainly scientific articles.

Throughout history, say the last 150 years or so, multiple theories (and ideas) were proposed, of which quite a few
are nowadays rendered obsolete. But, what we have today, are (at least) 7 or 8 serious approaches which promote
the idea of parallel- or multiple universes.
Although the community of physicists is quite divided on those different ideas, there exists up to this day, no fundamental
'proof' against any of them. This is ofcourse not to say that any of them might truly reflect 'the state of affairs'.
Certainly not. Ofcourse, as another thing, having 6 or 7 theories also mean that they cannot be all true at the same time.
So, most have to be wrong, and will possibly be proven to be nothing more than an "interesting idea", at a later time.

For now, we simply have no truly conclusive "evidence" that one of them is on the right track.
However, the general idea among physicists is, that some ideas are way stronger (eg. chaotic inflation) than others (like Everett's MWI).

Ofcourse, contrary to all of the above, a fair number of physicists (or scientists in general), do not consider
"parallel universes" or "multiverse", as a serious option at all. Or maybe that's even the larger part of scientists.

It's not impossible that experiments performed in the coming years will make a strong point for a certain theory.
For example, some Cosmological Brane-world scenario's also predict certain particles/fields (undetected up to now),
that might potentially explain "dark matter" or "dark energy" (true physical concepts). It's not impossible that
coming LHC experiments will provide strong pointers for the existence of such particles/fields.
By the way: The LHC is currently the world's largest particle acclerator.

So, let's see what we are dealing with...

I simply randomly picked a theory to start with, and I will gradually work (briefly) through all of them.
Let's start with the older "Everett's MWI" theory.

1. Everett's "Many Worlds Interpretation MWI" (1957).

A great physicist once said: "Nobody understands Quantum Mechanics".

Ofcourse we might be able to apply the rules of a certain mathematical framework, but that does not mean
we truly understand what is really behind it. So, many wonder on how we must interpret Quantum Mechanics (QM).
Even today, there is still no absolute answer. At least, the following important interpretations exists:

Table 1:

-The Copenhagen interpretation.
-QM with Hidden variables
-Decoherence as a successor to the Copenhagen "collapse"
-The Many Worlds Interpretation (MWI) -a multiverse theory
-The Many Minds Interpretation -a "light" multiverse/multimind theory
-Poirier's "Waveless" Classical Interpretation (MIW) -a multiverse theory
-The transactional interpretation
-de Broglie - Bohm "Pilot Wave" Interpretation (PWI)
-possibly also the "Two State Vector Formalism"

It's a remarkable long listing indeed. If you would like a brief and very simple overview on most of those interpretations first,
you might like to see this note.
That's one of my notes, so it certainly is not "great" or something, but at least it's short (and hopefully not too boring).

In this section, we will briefly focus on Everett's (and Wheeler's) "Many Worlds Interpretation" (MWI).
It stems from around 1957, and it is indeed a true Parallel Universe Theory. It needed a couple of years "to sink in"
in the community of physicists.
The way I see it, from around 1965 to about 1985, it was a very serious competitive theory amongst all other
interpretations. I would say, that in it's "best years", probably over 30% of physicists gave it serious thought
and a relevant fraction of those physicists even believed it was the best we had.
However, from (about) 1990 when Zurek's interpretation of "Decoherence" truly got momentum, MWI lost popularity. Even without
considering Zurek's "decohrence" paradigm, many scientists gradually discovered more and more, that MWI lacked
a true "oncology", and that it actually focussed too much on the objective "wave function" (or statevector) itself.

I would say, that from around 1995 (or so), more and more studies appeared which all made it quite likely that
it's really difficult to sustain MWI as one of the best candidates anymore, and that it even might be flawed,
but the latter was (probably) never really proven.

I must however hastely add that MWI still has a certain base of supporting scientists.
To make that a bit stronger: regularly (even today) new articles are published which makes a case for the MWI theory,
so, if I made the suggestion that MWI is "nearly dead", this is by no means true.
However, the supporting base of physicists supporting MWI, seems to be decreasing, since, say, 1995 or so.

The "orthodox" interpretations in QM:

There is no such thing as "orthodox" QM, but I need some means to distinguish between the "traditional ways"
to look at QM, like the Copenhagen Interpretation, or Hidden variables, and the ways to treat QM
in the context of parallel universes. Therefore, theories which explicitly uses parallel universes or "many worlds",
I would call "non-orthodox" interpretations in QM.
Ofcourse, it's quite hard to sustain that a theory like the "pilot-wave" (of de Broglie-Bohm) is really "orthodox", since
it's certainly not. However, it does not refer to "Many worlds". So, I hope you get my idea here.

So, let's first take a quick look at a typical orthodox description:

Let's suppose we have a fictitious Quantum System that we can represent by a "vector" (or State vector).

|Ψ>= a |BOX1> + b |BOX2> + c |BOX3>   (equation 1)

This fictitious Quantum System (say the position of a particle), is a superposition of the three different states
|BOX1>, |BOX2> and |BOX3>, meaning..., yeah... Meaning what????

In the Copenhagen interpretation it is said that there is a chance that when a measurement takes place, we may
find the particle either in BOX1, or BOX2, or BOX3, with probabilities for which hold |a|2 + |b|2 + |c|2=1
The latter equation is not strange, since all probabilities must add to 1 (or 100%).

But equation 1 is strange. Does it mean, before we performed any measuerment, that the position of the particle
is in BOX1, and BOX2, and BOX3 simultaneously?
Yes, indeed. This is very strange, since we have no classical equivalent for something like this.
However, for example the QM solutions for the position of an electron in a Hydrogen atom, is quite similar to what we have above.

But here we have a measurement problem. The moment you open the boxes, and say, you find the particle in BOX3, what
happened to the superpostion (expressed in equation 1) ?
The Copenhagen interpretation now postulates that the Statevector (like equation 1) "collapses" into one
of it's basis states, like |BOX3> (also called "eigen" states).
Here we have a real problem in QM, and facts like this one, triggered lots of people to ponder on how to interpret QM.

Most notably, in the twenties, thirties of the former century, there was quite some opposition to the Copenhagen view.
However, some of the people who favoured it, quite often saw it as just a "working" methodology, since it worked.
But, many were not happy at all, and for instance Einstein proposed that QM is "not complete".
It also lead somewhat later to the postulate of "Hidden Variables", that is, variables we do not know yet, but if we would known them,
it would remove all "vaque-ness" and made QM deterministic again.

By the way, in table 1, you can see quite some alternatives for the Copenhagen interpretation, like for example the "Pilot Wave"
interpretation of de Broglie, which was leter picked up by Bohm again.
Or explaining Quantum phenomena using the idea of "hidden variables", in such a way, that if those variables were know,
we would have a deterministic theory again.

By the way, equation 1 shows a statevector which is expanded in 3 basisstates. In general, when dealing with "n" dimensions
with respect to the number of basisstates, we have:

|Ψ > = c1|a1 >+ c2|a2 >+...+ cn|an > = Σ ci |ai >   (equation 2)

In QM, people often speak of a complex "Hilbert space" where |Ψ > is member of.

Everett's Many Worlds Interpretation (MWI) of QM:

Around 1957, Everett published his Phd thesis, "Relative State Formulation of Quantum Mechanics", which was more or less
the Grandmother of parallel universe Theories in QM.

In short: The Many-Worlds Interpretation of QM holds that there are many worlds which exist in parallel in the same SpaceTime
where you are part of. In many cases, where Copenhagen would talk of the (strange) collapse at a measurement, in MWI
the current Universe "forks" into new chains of events. In a sense, the Theory is "deterministic" if the mechanics of how
the "forks" work, would be well explained.

Please note that Everett's original arcticle was called "Relative State Formulation of Quantum Mechanics", so for
Everett, an absolute state does not exist, and we are always dealing with "relative states".

He, more or less, reasoned along the following lines. Taking pure wave mechanics as the basis, he seems to fundamentally rejects
the "collapse" of the statevector to an eigenstate when a measurement takes place, since the mechanisme behind it,
is not explained at all. Further, for Everett the Wave function (or State vector) itself, is a physical reality.
Also, superposition of states exists as well. Next, Everett then makes a remarkable observation that no subsystem
exist "just by it's own" but the collection of subsystems are not independent, but correlated.

Using a view of composite systems like a Quantum System and measuring devices, he shows that a "jump" to an eigenstate
is relative upon the mode of decomposition of the total wave function into the superposition, which actually means that any found
result state is "simply relative". He further shows that such a process is continuous, and thus will not stop.

There is ofcourse a mathematical framework in his original article. I do not repeat that here, ofcourse.

It is further extremely interesting that there really exists a "pre-seed" for "decoherence" in Everett's theory.
Secondly, at some point Everett's also refers to the memory imprints related to observers. He literally writes in his article
that (quote) "....the machine has perceived A" or "the machine is aware of A" if the occurrence of A is represented in the memory,
since the future behavior of the machine will be based upon the occurrence of A...." (end quote).

In the article, Everett sees as likely that a measuring device might experiences outcomes A, B, C etc..
while based on his relative states formalism, depending on the mode of decomposition of the superposition, any legal sequence
of other outcomes could be possible too, and actually instantiates or branches off independently.
In effect, at any event (like a measurement) we have a definite observer state and a corresponding system state, but that's no more than
a branch from the potential in the superposition.

Everett further never refers to parallel universes or something similar. For him, the key words are "splitting in branches",
and this formalism was somewhat later called "Many Worlds" theory, and that "label" sort of kept stuck.

Simple pictorial description of Everett's MWI:

If you did not liked the discussion above, I have a simple, very short (but a bit flawed), pictorial description of MWI:

In a simple pictorial representation: Suppose we have a particle, and let's represent it by a "coin".
Ofcourse, this coint can be expanded in sub-coins (or basis coins), just like equation 2 above shows us.
So, our coin is a "superposition" (just like, for example, 1 euro is 10 x 10 cents, or 5 x 20 cents).

MWI acts like having that coin (the superposition), which is a large set of (sub-) coins (the subwaves),
and when you throw them away, they all roll into different directions, all acting differently with their own parts
of the environment.
Every such sub-coin, is now branched off into it's own "world".
Ofcourse, we need a bit imagination here, and just think that all those "private" parts of the environment,
which interacted with the nth (sub) coin, is now completely detached from the other parts of the environment.

(Allright, it's not great, but it's no more than just a humble attempt... I understand, if you don't like this too).

2. Hubble Volumes.

This time we go for the very.. very large...

I wonder in how much you will appreciate this section as a "Theory of parallel universes", but a fact is,
that many folks indeed do so.

Although I will refer sometimes to "Inflation" in this section, "Inflation" is so interesting that I like to.
discuss it in another chapter more thoroughly.

Even in the early years of the former century, it was theoretically made plausible (Friedmann), that the Universe
was expanding. Ofcourse, that was already implied by the GTR equations of Einstein, however, Einstein rewrote
his equations in order to have a steady state Universe, which was the dominant view in the twenties.

Somewhat later, Observational proof of the epansion was became really solid, when Hubble presented his "redshift" findings,
which made a real case for an expanding Universe: it seems to get larger all the time.
Well, you may wonder if that last sentence is a "good phrase" anyway. Reality maybe somewhat more complex.

The "history of science" is so much fun to study, but I have to stick to the real point of this section.

It is quite certain that from around 1950 (or so), it was mostly accepted that we have to deal with an
expanding Universe. That is, starsystems like remote galaxies seem to recede from us, and a peculiar thing is that they
seem to recede faster, the larger the distance is (from us).
For the larger part of the second half of the former century, questions remained like, for eaxmple, will the expansion
slowly decellerate at some point. Or, is it possible that the expansion comes to a halt, and that the Universe will undergo a Big Crunch again?
Or will it simply expand forever...?

Many of such questions were alive among cosmologists, and important pointers were under study like the "mass-energy"
distribution, and if SpaceTime was curved on a large scale etc...

At some point, folks started to realize that the "seemingly" enormous velocity of very remote systems, may have
a completely different origin. The velocities were based on the large "redshift" of the light of those remote systems,
just like the doppler effect for moving objects. However, the same effect occurs if space is created along
any direction. You probably know that famous example of a baloon, with dots on the surface (representing galaxies),
and when you inflate the balloon, all dots recede from each other, due to the fact that the balloon's surface expands.

Even at this "point", using the theory sofar, it makes sense to investigate the "horizon", or "Hubble volume".

But we can even put some more fire into the discussion on expansion.

Around 1998, a rather comprehensive study started to measure luminosities of several "Type Ia supernova's"
which are "exploding" stars, but which have proven to be very accurate "candles" with a very definite luminosity.
They can be very useful to determine "distance/redshift" relations.

After sufficient data was accumulated, interpretations seem to suggest that the luminosity of more remote supernova
were actually (and this is the crux) dimmer and more redshifted than expected.
Ofcourse, the actual techniques are much more involved, but typically, the results are often shown in graphs which show
the observed magnitudes plotted against the (socalled) redshift parameter z.
The plots thus aquired, seem to suggest an accelerated expansion, instead of a expansion which slowly decreases.

So, at this moment, most cosmologists believe that the Universe undergoes an accelerated expansion.

The source which drives that expansion still puzzles many physicists and cosmologists.
Several candidates were forwarded, as for example an intrinsic pressure in the Vacuum, or an still unknown field
called "quintessence", or possibly some other source.
In general, the still unknown agent behind it, is collectively labeled as "Dark Energy".

While SpaceTime expands everywhere, for our local part of the Galaxy, there thus exists an event horizon
which is that distance from us, so that light (or information) from still more remote places, cannot reach us anymore.
There simply is too much expanding Space between us and this "event horizon".

In effect, this 'event horizon' defines a "region" (similar to a sphere), which is called a "Hubble Volume".

For anything beyond that horizon, we cannot receive information.
Some people also say that we actually dealing with "causal disconnected regions".
Also, some rephrase that as that we are living in our own "patch of the full Universe".

But, what is the connection with "parallel universes" or the "multiverse"?
Above it was made likely, that we are in our own "patch" of the Universe, or Hubble volume, which is bounded by
an event horizon. Beyond the horizon, given the data and observations we have today, similar conditions would apply.
Hence, far beyound our Horizon, it would be likely that at those places we have similar SpaceTime with the usual
"content" as we have "here" (Galaxies, clusters etc..). However, those far places are fully out of reach (even for light,
or any other forms of information exchange), and thus some folks talk about a "multiverse" or "parallel universes".

3. Poirier's theory of interfering "classical" universes (MIW).

The seemingly "probabilistic" behaviour of quantum obervables, might be due to an idea nowadays
called the "Many Interacting Worlds (MIW)" theory.

The QM model devised by Poirier, originated somewhere around 2010 and went through further elaboration,
especially in cooperation with Schiff, and ended in about 2012 in something what's now called MIW.

I must say, that at this time (and it might seem a bit strange), it's not fully clear to me who first re-introduced
almost classical Physics into the dicussion of "interpretations of QM", and who actually introduced MIW.
Ofcourse, I have to say quickly that the Broglie-Bohm (pilot wave) interpretation uses many classical features as well.
However, in MIW, it truly goes one step further since each independend "world" in MIW, is fully ruled by classical physics.

About the origins of MIW:
It seems that Holland, Hall, and several others, do or did rather similar work as Poirier.
But, someone like Sebens also recently launced similar ideas as MIW.
But they all operate closely in the same "arena", and since most scientists seem to attribute MIW
to Poirier, from now on I will take that as a fact.

Considering the basics of the "Many Interacting Worlds" theory, You might see a parallel (no pun indended) to Everett's
"Many Worlds Interpretation" (MWI), but that would not be correct.

There are fundamental differences. Most notably:
  1. In Everett's MWI, the wave function is real and plays a central role. In MIW, the wave function does not exist,
    and in fact MIW is a sort of QM "without the wavefunction".
  2. In Everett's MWI, universes branches off due to the fact that superimposed waves each interact with the environment.
    In Poirier's MIW, there is no branching, no wavefunctions, but the many worlds may "interact".
  3. Everett's MWI uses standard Quantum Mechanics (wavefunctions, probabilities etc..), however Poirier uses established
    rules from many parts of physics, whereas many are simply familiar classical, like trajectories, position/impuls, Lagrangian etc..,
    where paths over different trajectories relate to the Many Interacting Worlds.
Most striking thus, is that in MIW, the Wave function with all its superimposed waves (states) is actually non-existent (!)
It's more an illusion, due to the fact that in Poirier's "Many Worlds", an observable might have
well-defined values in different "Worlds", that is, each "World" it has it's own "private" values for that observable,
but since there exists variation between "Worlds", we percieve the illusion of a composed State vector where the same
experiment might show different values all the time.

So, if you like, you might say that there is no fuzziness in Poirier's theory: for example, particles do occupy well-defined
positions in any given world. However, these positions vary from world to world, and thus explaining why they appear
to be in several places at once. That we observe that, is due to the fact that (according to MIW), nearby "Worlds" interact.
It's that same interaction which makes us believe in the spreading of wavepackets and for example tunneling through a potential barrier.

In MIW, each world evolves according to classical Newtonian physics. All (illusionary) quantum e?ects arise from, and only from,
the interaction between worlds.

What are the "Worlds" in Everett's MWI and Poirier's MIW?

In MWI, it's not too hard. Everett only talks of "relative states", and the branching occurs when the superimposed waves
interact differently with the waves of the environment. Although quantum probabilities still hold, another key element of which
we must bee aware of, is that if SubstateA has a certain propbability, and SubstateB has a another probability,
each can "branch off" at interaction, and start a "life" by their own. Think of them as initially as orthogonal, and start their own
different projected life in the environment (where that microscopic environment is affected too ofcourse).
It's like having a coin (the superposition), which is a large set of (smaller) coins (the subwaves), and when you throw them away,
they all roll into different directions, acting differently with the environment.

In MIW it's a tiny bit more delicate.

A rather simple way is to take an aspect of the "Broglie - Bohm" (pilot wave-) interpretation as a starting point.
If you would have "n" particles, then you might define a (one) "configuration space" for that set of particles, which space
can be described by the vector {q1,q2,...qm} where m is larger than "n" since we might
review our particles in several dimensions (like 1, or 3, like our normal 3D distance space).

It's important to keep in mind here, that we use one configuration space for those "n" particles.

When physicists work out such a model, then positions, and momentum, and other characteristics of the particles can be described
in such a framework.

The rather "bold" assumption in MIW is, that not only one "configuration space" might be possible, but say "J" spaces
and even J going to infinity. That's rather new, to say the least. Now we have "J" spaces, where each "j" in J, defines
a configuration space, where each one "j" describes all the positions and momenta of those "n" particles.

-So, suppose we have j=j1, then we have a certain "configuration space", descrbing the positions
and momenta of "n" particles.

-And, suppose we have j=j2, then we have another "configuration space", descrbing the positions
and momenta of the same "n" particles, but in effect with different positions and momenta compared to j=j1

Did you noticed for example the different positions for j=j1 and j=j2 (and all other "j" from J)?

When physicists further work out such a model, then positions, and momentum, and other characteristics of the particles
described by one "j", like j=j1, might be affected by characteristics of the particles from another configuration space,
like j=j2.

It can be further made likely, (using some math) that "close" "j" from the space of J "configuration spaces", tend to work
repulsive, so that the illusion is created that, for example, we are dealing with a spreaded wavepacket as a particle.

I hope this conveys at least a "glimse" of the heart of MIW. Actually, you might say that MIW turned QM around to be classical again.

4. Inflation with bubbles / eternal inflation / chaotic Inflation.

It's probably hard to believe that "an awful lot", (that is, the Universe), can come from "nothing" (or from "almost nothing").

The following has not much to do with inflation, but we may take a short excursion to one of the Heisenberg
uncertainty relations, which is a remarkable fact in QM.

The particular relation I am talking about, describes an uncertainty in "Energy" and "Time".
The relation say that in the microscopic domain, energy can be obtained from the vacuum as long
as the following holds: ΔE.Δt ≥ ħ/2 (where E is Energy, and T is time).
So, you can borrow energy for a certain timeslot, as long as it is returned later on, according to the relation.
The socalled microscopic "quantum fluctuations" are believed to exist literally everywhere in our present SpaceTime.
One such manifestation are the "virtual particles", which popup from the Vacuum, and destroy each other again, only
existing for a very brief moment.

The section above, has the advantage that we now are introduced to the concept of "quantum fluctuation",
in case you was not aware of it.

As of around January 1980, Alan Guth started talking openly on his new ideas of the origin of the Univere.
Then, in January 1981, a (nowadays) famous article was published (Physical review D), which beared the title:

Inflationary universe: A possible solution to the horizon and flatness problems.

This theory explained the birth of the universe in a unique and completely new way, and at the same time avoiding the
problems as mentioned in the title of the article. His theory of "inflation" was pretty good in describing the most
extremely early phases (like as from 10-38 second to 10-32 second, and a tiny bit later on),
but it did not correctly handled some later phases, as Guth admitted.

However, it was already a major step from the earlier "Big Bang" proposal, which presumed a strange superdense,
superheated singularity, which for some reason, "exploded" and ultimately formed the Universe as we know it today.
However, as people see it often today, is that when the Inflationary period ends, the next phase then fits the traditional
"Big bang" well, so it is nowadays often interpreted that the Big bang follows afer Inflation.

It was only a few years later (1983) that Andrei Linde proposed a revamped approach, and actually cured
the major problems in the original theory. However, Linde's approach, actually made eternal inflation,
or a bubbled Multiverse (multiverse=multiple universes), very likely.
So, for my purpose, that's a very interesting item to discuss.

The basic idea behind Cosmic Inflation:

If there is really "nothing", then there is no space, and no time. In effect, you might say that it's useless to ask "what was before"
since, time does not exist. So, the notion of "before" is non-existent. If you like, you may visualize it as if space and time
are both spatialized, but "0".

Modern theories try to unify the known forces in our present day Universe, and also try to unify fundamental
theories (like QM and gravity). It is expected that at extremely small scales, all the fundamental theories "converge"
to each other, and thus unify. In that sense, it may well be so, that that QM effects and Gravity are then very "close".

Now, the absolute "bootstrap" of the start of Inflation is still not solved, but it is often argued that in a period
around a period of 10-42 second (or so) from "0", a quantum fluctuation occured and it entered into a precursor of gravity.
Once gravity exists, in whatever form, a certain format of Vacuum exists then too.

This extremely short period is sometimes referred to as the "Planck epoch".

Guth's theory states that this 'pre-space" is equivalent to an extremely small patch of "false vacuum" which theoretically
is the same as "negative pressure", or "positve gravity", which is a repulsive gravitational field

Note: Maybe "positive" and "negative" pressure are confusing, but pressure behaves very much like gravity.
A positive pressure namely, equates to an attractive gravitational field. A negative pressure is repulsive.

The "negative pressure" or repulsive gravitational field is the driving agent behind Inflation. The patch expands
exponentially since nothing holds it back. Secondly, since the false vacuum does not have anything to interact with,
the energy density stays the same, while the total energy increases. Inflation in that respect works like a magnifying glass.
Now, energy conservation says, that if the total energy in the patch increases, that must be equal to the "work" done
by the repulsive gravitational field, that is, the expansion itself. It seems as if "Inflation drives itself...."

Such a scenario looks, as if Inflation will never stop. There are some intracies indeed, and by the way, the number
of Inflational theories (since 1981) is quite large, each dealing with several subphases.
Guth further assumes on good grounds, that the Inflationary period itself is somewhere from 10-39 to 10-31 second.

For now, we assume (as Guth) that the false vacuum went instable, and the false vacuum energy is released by "snowing" (condensate)
elementary particles (quark-gluon soup) from the vacuum.
Generally it is understood that the change of the false vacuum to "true vacuum" (or steps in false to less false), have lead
to particle production.

This phase is sometimes referred to as the "quark epoch". We are now still only about 10-12 second from the absolute beginning.

That phase is ofcourse much more involved than my few line of text. For example, it's assumed that several forms of "symmetry breaking"
occurred, as the tempurature lowered, resulting in the basic forces as we know them today.

When the universe was about 10-6 seconds old, again, the temperature (energy) was lowered enough for quarks to bind
into hadrons (hardron epoch).

Several other phases followed, like the lepton epoch.

How complex the various phases can be, is also illustrated by the fact that once matter and anti-matter existed, but Nature
seemed to have had a slight preference (bias) for matter (instead of anti-matter).

Noteworthy is then the fact, that, a long time later, about 380000 years after the birth of the Universe, the temperature has
dropped sufficiently for leptons and protons to form (mainly) hydrogen, and at that point, the Universe became transparant for light,
or electromagnatic radiation in general. This is the source for the "relic" "Big Bang" background radiation.

The Horizon and flatness problems:

1. The Horizon problem:

It might be interesting to spend a few words on those problems, which were probably solved by Inflationary Cosmology.

The fact that our observable Universe is so large, places us for some problems, using a traditional Big Bang scenario.
Very distant regions, cannot contact other very distant regions, to exchange information, like heat, or other forms of radiation.
One problem (among other problems), is that the "relic" "Big Bang" background radiation (also called the 3K cosmic background),
is very accurately the same in all directions. In the traditional "Big Bang", this would not be the case. There would have been
considerable fluctuations.

In the Inflationary model, the initial false vacuum patch prior to the inflation, can be seen as very small
but causally connected region. In other words: uniform.

The inflationary epoch, evolved so extremely fast, that the homogenity was completely freezed, and that effect
we can still observe today in that famous uniform cosmic background radiation.
Thus, an original problem in the "full" Big Bang scenario, is often regarded as a "pro" for Inflation.

2. The Flatness problem:

The "full or original" Big Bang scenario poses another famous problem: the flatness problem.
This is usually expressed by, and related to, the "critical density" Ω, for which hold
that Ω can be "< 1", or exactly "1", or "> 1".

Suppose the actual density is denoted by ρA, and the density for which the universe would be flat, as ρF,
then the ratio Ω = ρA / ρF functions as a normalized density: the "critical" density.

Below is an simple argument, based on the traditional mass-energy in the Universe. However, how exactly "dark matter"
and "dark energy" would influence it, is a very important question. However, I stick for now to the (say) traditional view,
because I like to demonstrate how Inflation solves the flatness problem, which would otherwise arise in the traditional
Big Bang theory.

The total density of matter and energy in the Universe, determines the curvature of SpaceTime.
In most conjectures, the General Relativity Theory (GRT) of Einstein, is the basis to start from.

Friedmann found a solution for the field equations of GRT. This solution shows a relation between
the gravitational constant, the speed of light, and some other parameters, and most importantly, the "curvature parameter"
(which is a measure for the rate of curvature of SpaceTime), and the total mass-energy density.

Three models come up from the equations of GRT and Friedmann: a (spherically) closed Universe, an open Universe, or a flat Universe.
Please note that here we are talking about the "geometry of the universe", that is, the sort of curvature of SpaceTime.

The "flat universe" means that we do not have a curved SpaceTime (globally), and that would only happen when we have
"curvature parameter" (k) to be 0. In that case, the critical mass-energy density Ω would be exactly "1".
Or, formulated more accurately: the ratio of the actual density to this critical value is defined as Ω.
Sometimes, for clarity in equations, Ω is rearranged to be the factor (Ω-1 - 1).
So, flatness then means (Ω-1 - 1)=0.

If we go back to " Ω" again, thus the ratio of the actual density to the critical value,
If Ω > 1, then we obviously would have a large mass-energy density and the curvature is positive,
meaning a (spherically) closed Universe. Probably, after a certain time, the Universe might collapse.

If Ω < 1, then we would have a too small mass-energy density and the curvature is negative, meaning
hyperbolic open universe (with respect to curvature).

Now, most atronomers/cosmologists think we have a "fine-tunings" problem, since large-scale observations very strongly
points toward a flat universe. So, Ω seems to be "1", which is rather special, probably too special....
Why would it be exactly 1? Why would the Big Bang ultimately end up with this very special density, expressed
by Ω=1 ? This question is the "flatness problem".

If Inflation would solve this, then the next question is: why would Inflation "make" Ω=1?

This could be answered, if the Friedmann equation would still hold at the inflationary epoch. If so, then
mathematically it can be written as (Ω-1 -1) x total energy = Constant.

Without considering the "cosmological constant" Λ, the equation actually is:

-1 -1) ρ a2 = -3 kc2/8πG

Above we saw that during inflation, the total energy ρ increases exponentially. Now, the rightside of the "=" is constant,
since it only contains factors like "c" (speed of light), "G" (gravitational constant) and some others.
To let the product in the leftside of the "=", be constant, while ρ increases, then the term (Ω-1 -1)
must decrease sharply while ρ increases sharply.

If this reasoning is correct, then Inflation makes Ω nearing the value "1", thus a flat universe follows.

I must say that this line of reasoning is not without critism, but anyway it's an agrument that's often heard to explain
the observed flatness of the Universe.

Above we have seen the first Inflation version from Guth. Next we will see Linde's interpretation, where the Multiverse plays
a key role.

The Follow up by Linde (and others):

Above we saw Guth's original Cosmological Inflation theory from 1981 (in a few very simple words).
By now, quite a few additional versions have appeared, by various authors, often focussing
on subphases (cooling and re-heating several times), and/or symmetry breaking.
Or, some later articles, also try to reconcile string theories with inflation.

Some newer inflational theory variants, expect a "multiverse", or multiple universes, to be a reality.
That's ofcourse very interesting for my note.

However, those newer theories themselves, and who was, or is, working on them, and when original ideas were expressed,
and how much "overlap" exists, is by no means very transparant.

Key terms anyway, are "eternal" and "chaotic" inflation. Sometimes, from the relevant articles, they look
pretty much similar. Well, at least for me that impression arose by now.
But "eternal" and "chaotic" inflation are not similar, as you will see below.

Also in those newer inflation theories, Guth himself is active. In a few rather recent articles, he proposes an "eternal inflation"
variant as a more complete theory, compared to the old (original) one. The multiverse is a collary of his central theme.
However, Guth was not the first who explored "eternal inflation", and it seems that Steinhardt and Vilekin were proposing
such idea's around 1983.

Linde seems more involved in something he called "chaotic inflation", and here too, the multiverse is a collary
of the central theme.

Already at this place, I like to say that something that looks (at first sight) completely different, namely "(string) Brane
World cosmology", might not be so "incompatibel" with those newer inflation theories afterall, according to some authors.
I like to touch that subject (that is, Brane World cosmology) in the next chapter.

Let's stick with inflation for now. Andrei Linde seems to be very connected to the idea of chaotic Inflation and a bubbled multiverse.
In 29 october 1981, an article appeared called :

A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy
and primordial monopole problems.

True, later articles, as of 1983, referred explicitly to chaotic inflation. and it seems that most people refer to those articles.

More players than only Linde are active in chaotic inflation, especially from 1983 up to 1990 (or so).

Here are a few words on Linde's initial interpretation:

Chaotic Inflation (Linde):

After a "quantum fluctuation", a scalar field exists, with a certain initial potential ϕ energy.
You can indeed make educated guesses about that initial value, expressed in Planck Energy units, but Linde primarily
keeps his theory generic.

The value of the potential energy, behaves like a harmonic oscillator. Depending on the initial potential ϕ,
Linde shows that the value of the potential can "roll-down" rather slowly, or possibly"roll-down" rather quickly.
This is actually the "chaotic" in the name of his theory, since using various forms of equations for the initial potential ϕ,
(like polynomials, or others) does not really affect the main theme of his theory. Inflation will inevitably follow.
Here, the term "inflation" simply means "exponential expansion", like as you can write the expansion as an "e function".

In effect, Linde wrote down a relatively simple second order differential equation for the potential ϕ,
where as a term the Hubble parameter (H=a'/a) is present too (here, a' means velocity, and a is distance.)

Amazingly, it simply follows that:

H=a'/a=mϕ/√6   with as a solution a=eHt.

True, this is the most simple form, and more involved ones exists too.
Whatever you say, the startling thing is that, using almost highschool physics, leads to an exponential expansion,
and further he shows that the theory is quite immune to the form of the potential ϕ.

Next, Linde argues that if we take a good guess of the initial energy, then in about 10-30 second,
the Universe inflates with an order of magnitude of 10100 (or so), meaning that the Universe was already
way way larger than what we today say is "the size of the observable Universe".
It indeed would explain why the Universe 'looks' flat, since, even if it was curved on a large scale, we would never
notice that in our small patch of the Universe.

At a certain "moment" ϕ is very small, and starts to oscillate around a "minimum". This is a particle
creation phase, where particles "snows" from the Vacuum.

Alright, now we understand what the "chaotic" means! This actually is Linde's main theme.
But next, he makes Inflation "eternal"....

Bubbled Multiverse, and Eternal Inflation (e.g.: Linde, Guth, Vilekin and others) :

During the inflationary period, small quantum fluctuations in ϕ were actually very likely, and when, nearing the ending
of inflation, ϕ got smaller, and those quantum fluctuations were the cause of smaller "density perbutations" which
many folks see as the cause for later galaxy formation.
This idea holds for virtually any inflational theory.

Chaotic inflation, at least according to Linde, implies a self-reproducing Universe. The reason for this
are "large" quantum fluctuations during inflation, which increased the value of the energy density in ϕ, leading
to larger perturbations, and substantial "faster" inflation of such region.

Some interesting scenario's are possible:

Some authors (but a minority) see here the cause for "topological defects" or "domain walls", which ultimately
will seperate those pre-universes. This is not a mainstream view anymore, but I like to mention it anyway.

Linde argues that those subregions expands faster than the original domain, whereas in those subregions, the same
type of "large" quantum fluctuations may occur, which again leads to expanding subregions.
This ultimately leads to a "bubbled" Multiverse.

Some authors even do not rule out that in fact we have "eternal inflation", since in the scenario above, it's not
simple to say that there have to be a grandfather inflationary period perse.

But even in the scenario of a "true bootstrap", the "bubbled" Multiverse is a theoretically defendable proposition.

Although also matematical conjectures exists, to illuminate the above (although they are likely not "perfect"),
do not forget, that in an inflationary epoch, according to GUT theories, gravity and QM are very close.
Thus, the assumption of larger "quantum fluctuations" is quite reasonable.

Are they Testable theories?:

Recently, "gravitational waves" were detected. It was a very large event, and you can't have missed it.
It was on the news everywhere.

It's quite likely (or better: quite possible) that "ripples" in SpaceTime are going to be detected,
which, after analysis and interpretation, might be an indicator of an endphase of inflation.

When the LHC is fully operational again, and those folks at Cern are able to let protons collide with 14 TeV (or so),
then again these will be experiments with a higher energy, and smaller crossection, and again it represents a peek
into conditions of an earlier Universe (than we had before).

It's not very difficult to extend this listing.

Are all physicists and cosmologists "believers" in Inflation? That's a "no".
Again, here too it's not difficult to provide reasons why not everybody loves Inflation.

Ok, I think I go to the next section now. The one after that, section 6, is about "Brane - World" cosmology, which originate
from superstring Theories. But I must say, that since quite some time now, quite a few authors try to fit (or reconcile)
Inflation wih those "Brane - World" theories.

5. The Universe as an emulation.

6. Brane - World Cosmology.

The subject is actually very large, and, I am really sorry to say so, but the math is rather killing.
I would say that there are only a rather low number of theoretical physicists/cosmologists, who are really deep into the math.
Ocourse, countless of other people have a good understanding of what it all means, and the significance ot the theories.

Let me start by summing up a few remarkable facts.

-Nordstrom - Kaluza - Klein (KK) theory:

The following is not the "birth" of string/brane theories, but it already contained an exiting core idea:
curled up, hidden (compact), "extra" dimensions.

Around 1916, Einstein published his Theory of General Relativity, which was a new way to describe gravity.
It's a unified description of gravity as a geometric property of space and time, especially the curvature of space.
In this sense, it's a 4 dimensional description using 3 spatial dimensions and the time dimension.

Around 1921, Kaluza developed an integrated (unified) view on Gravity and the Electrodynamic theory of Maxwell.
His idea rests on a five-dimensional spacetime framework, thereby using one additional spatial dimension.
As said above: The objective was unification of gravitation as described by Einstein, and electromagnetism as
is decribed by the Maxwell equations. It's very remarkable to see how the KK theory can be "projected" to 4 the dimensional
descriptions of the Einstein relations, and the equations of Maxwell.

The spectacular thing is ofcourse the addition of Kaluza (using Nordstrom's idea's) of an extra spatial dimension.
One problem however, was the fact that this "extra" dimensions seems to be unobservable. For Kaluza, it was only important
to have that extra dimension, for the math to work, so, even if it was only extremely small,
then that's ok for Kaluza.

Slightly later, Klein suggested that this extra dimension, is "curled up", like an unnoticable small tiny circle, so that the
World "looked" 4 dimensional (3 spatial + 1 time dimension), while it actually was 5 dimensional (4 spatial + 1 time dimension).

Although at that time, it all was an extraordinary theory, it did not recieved much attention. Only much later, the work of
Kaluza, Klein and Nordstrom was better appreciated.

There is a parallel to present day superstring theories. One such parallel is the fact that, according to superstring theories,
the World must have D=10 dimensions (in unifying M-Theory, it's 11).
Thus meaning 9 spatial dimensions. Here, 3 are the extended ones we are so familiar with, while 6 others are "hidden",
that is, so incredably tiny and "curled", that they are fully unnoticable.

The idea of replacing "point" particles by "strings", which have a small vibration in those extra dimensions,
seems like a great idea, as is illustrated in the next paragraph.

-Divergence and renormalization: