A very simple note on "Inflation and B-mode polarization".

Version : 0.3
Date : 13 April, 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.



Halfway march 2014, it was announced in almost all news shows around the Globe, that finally quite convincing proof was found
for the "Big Bang", which created our Universe. You can't have missed it !

But what exactly did they find, and what does it prove? This small note tries to adress that question.


1. In a nutshell (no doubt a bit "clumsy").....

In the next few chapters, we will go into more detail. However, here the main points are presented in a few words.
But, since I try to give a supershort intro in this chapter, the text no doubt will be a "bit clumsy".

As it is, many cosmologists believe that the very first phase of the Big Bang is the socalled "Inflationary Period", which means
that from a "near zero sized", Singularity, space-time was created in an un-imaginable superfast exponential rate.
The driving mechanism to this, that is, to inflation, is a sort of "negative pressure", resulting in superfast creation of space-time.
Ofcourse, the nature behind this "pressure" is not explained right now. We will come to that later on.

Alan Guth himself (one of the two originators of the theory), used the following simple analogy to illustrate the creation of space-time:
Imagine a handpump. Now, inside the tube, we have a piston. (Please ignore everything in front of the piston.) Now if pressure is exerted,
the piston moves, and "space" is created behind the piston.
Ofcourse, the analogy is *certainly* not perfect, but it tries to relate negative pressure to space-time creation.

Now, quite a few 'Inflationary theories" exists, which all differ in relevant details. But the main theme is like this:

The first fractions of a second at the birth of the Universe is dominated by inflation. But, as time progressed, and the Universe cooled down,
at much later phases, elementary particles are formed.
Before particle creation, the Inflational period is thought to have reached it's final stage, and the Universe enters (more or less) the traditional Big Bang.

While the Universe cooled down still more, at about 380.000 years from the "start" another remarkable event happened:
Then, protons and electrons "recombine" to form Hydrogen atoms. This is an important event, since this "more or less" made the Universe "sort of"
transparant for light. Before this event, just consider the Unverse as being foggy, or blurry, and not free for photons.

As the Universe cooled down further, the background thermal radition dropped down as well. Presently, it's about 3K in all possible directions
where you would measuere it. Now, the Universe should have an age of about 13.6 billion years, according to the models. If we "look back", and
create a map of the background radiation, it's almost completely uniform.
Remember the event where Hydrogen atoms were created? With resepct to the thermal radiation, elementary particles did no longer scatter
or absorb it any more, and so the universe became transparent to this radiation as well.

The various maps of this radiation, corresponds to the time as the Universe was at an age of about 380.000 years,
where it became transparant for light. So, you might say it's the first "free" light of the Universe.
It's important to keep in mind that thus those maps reflect the state of the Universe when EM radition "got freed".

Fig. 1. The WMAP data.


Later on, more precise maps were constructed, as more detailed releases of the WMAP data became available.
WMAP is data from a NASA Explorer mission, that was launched June 2001.
Here, tiny fluctuations in temperature are visible. This map (shown in fig 1) represents the complete sky.

Although the picure shows clear variations in colour, the actual measured differences in temperature are very small.
You can easily find large detailed pictures, if you just google on WMAP (e.g. Nasa, wikipedia etc..)

Still more accurate attempts were undertaken in order to get more details from the primordial radiation.

Already in 2002, the polarized E mode component (of the background thermal radiation) was detected, with fairly accuracy.

Polarization is a measure for the orientation of the EM field of light (or ElectroMagnetic radiation in general).
Also, for now, take for granted, that radiation or light, might be stretched or compressed due to various reasons,
also if space would be bended like compressed or stretched.

Indeed, halfway march 2014, the great discovery was announced. An observatory near the South Pole, did very accurate measurements.
The data gathered, was done using the BICEP2 method and devices.
This time they found "vortice-like" or "spiral-like" B-mode polarized components in that primordial background radiation.
This was major ! There exists several mechanisms as to why the "vortice-like" B mode components are detected, but the data
for now, seems to suggest that we see the effects of gravitational waves which can strech or compress space-time.

Fig. 2. BICEP2 data.


As you might know, gravitation bends space-time. So, the effect seen might be well due to gravitational waves compressing
and expanding space-time, resulting in the "curly" BICEP2 data.
This fits rather well in selected Inflationary Universe models. Hence the fact that this discovery is strong supportive
material for Inflation, and thus for the "Big Bang" model.

It does not prove Inflation, but most cosmologist and (theoretical) physicists see it as supportive evidence.
It's also noteworthy that we probably have "seen" gravitational waves for the first time.

So, we might say that the "ripples" as observed, are nowadays linked to gravitational waves, in such a way, that it is
supportive for the "Inflationary Universe" theory.

You might see it this way, that Inflationary Theory, has as a collary, those "gravitational waves", which now has been observed.
And the proof of it, are those "curly" B-mode polarized components of the thermal background, which strongly suggest "rippled" or
streched and compressed spacetime.

Although the observations stirred the scientific community, it's fair to say that a bit time is needed for that community to
proper evaluate the results and evaluate it's implications. But for now, "it looks good" for the Inflationary Theory.

Next, let's try to explore "The Cosmic Inflation" a bit further.



2. A note on Inflation.

I am afraid the following will be a rather lengthy text.

Inflation is not the only theory which has fans to explain the origin of the Universe. Some folks, active in the field of "superstring"
theories, have placed their dollars on "Colliding Branes" theory, and indeed, some other theoretical ideas linger around too.

Somewhere around the late 20s/30s of the former century, it was more and more established that deep-space galaxies are showing a red-shift
in their spectrum, which suggested they all "flew" away from us. Moreover, it seemed that this redshift was proprtional to the distance,
suggesting that the further away, the faster they go. It looked like a "linear" relation, like established by Hubble.
Now, we are not going in historical details at all (which are fabulous to read). But since everyting was fleeing from each other, it was
quite natural to suspect a common origin: the Big Bang.

Note: already in 1922, Alexander Friedmann proposed that the Universe might be expanding. That was in a time where Einstein had
placed a "constant" in his GRT equations so as to support a "static Universe". However shortly after, Einstein reconsidered that viewpoint.
But, much more good observable and factual information to support "expansion" came since the 50s.

Nowadays, it's commonly accepted that space itself expands, which is responsible for the observable fact that deep-space milkyways
show higher redshifts, simply due to the fact that all space expands.
Often, the analogy with a 2 dimensional balloon surface is used. If you draw some dots on the surface, and inflate it more,
all dots seems to move away from each other.

But, the original Big Bang could not explain some "classical problems".

Usually, most people start talking about Inflation, as a solution to those "classical problems" like the "Horizon problem" and others.
Ofcourse, I will do the same here.

2.1 The Horizon problem:

The Universe is rather large. The observable Universe is about 13.6 billions lightyears. However (and possible some folks are amazed
to hear this), the actual Universe is way, way, larger ! If we observe a deep-space galaxy at 11 billion lightyears distance, then we "see" this object
as it was 11 billion years ago. In that timespan, from "then" and "now", the actual "distance" has increased dramatically.

Actually, for very far away objects, any causal relationship is gone. Since space is continuously created, information between the objects
cannot be exchanged anymore. They are beyond each other horizons. So, an observer in such a milkyway, can't receive the EM radiation (or other type
of information) from the other milkyway. There is too much expanding space between them.

Such a reasoning has lead to the notion of "causally disconnected regions".

Some cosmologists say: "we live, and can only see, our patch of the Universe".

But even in our patch, the background thermal radiation is remarkably the same, in any direction, everywhere (except tiny fluctuations).
But that's not all. Although the distribution of clusters of milkyways (galaxies), as we observe it today, is in "filaments" with holes in between,
that is not what we mean here. What we mean is that the properties of space, the Vacuum, with it's physical constants, is highly uniform
across our patch.
Actually, this is remarkable. No sort of Bang will result in that uniformity of space.

There is also another way to look at the Horizon problem.

Again, consider galaxy "A" (a milkyway) at 11 billion lightyears distance. This object is close to our Horizon.
Suppose we see galaxy "A" in the direction of the galactic Northpole (a direction perpendicular to the disk of our own galaxy).

Also suppose we see galaxy "B" in the direction of the galactic Southpole (a direction opposite compared to above).
Galaxy "B" is also around 11 billion lightyears distance (as it was 11 billion years ago).

Since the Universe is only about 13.8 billion years old, signalling (or exchange of information), could never have taken place.
Still, the background thermal radiation, and properties of space/time, are (were) quite the same at "A" and "B".
But "A" and "B" are far beyond each other's Horizons. But both are just within our horizon.
It seems that it can only be explained by Inflation, which at the end of the epoch, left an isotropic/homogeneous Universe.

The Horizon Problem is just one clue as to why "inflation" might really be such a good model. Inflation goes more or less like this:

2.2 The original Inflation theory (in terrible clumsy words):

From a (pretty much unknow) super energetic Singularity, a quantum fluctuation occurred. From a extremely high energtic level,
the Sigularity "decayed - rolled down - unfolded" almost instantaniously into a false Vacuum with certain metrics (size).

This false instable Vacuum, holds a "positive" vacuum energy density, which equates to a "negative vacuum pressure".

The period in which this occured, is thought to be about 10-33 seconds. The sized increased dramatically during this period.
There is not too much consensus on estimates on how large the Universe actually has "grown in size", during this Inflationary Epoch.

Anyway, the Inflationary epoch created a metric of space/time unbelievably faster than the speed light.
This is not a violation of Einstein or causality. There was just nothing to refer to before. From a metric of zero (or almost zero?),
a certain domain of false vacuum was created. This Rollout of space, was so fast, that during the epoch, only space/time was created.
This explains why the state was so "uniform" after the Inflationary Epoch.
It is commonly accepted, that the Inflationary Epoch then now almost is to it's end.

Key point is, that inflation created space (false vacuum) so fast, that it had uniform properties everywhere.
Note: not all cosmologists and (theoretical) physicists fully endorse that view.

This space/time was actually synonymous to an instable False Vacuum, with a higher Energetic Potential than a true Vacuum. Some cosmologist call
that false Vacuum, to hold the "Inflaton Field", in a intrinsically unstable situation.
At that moment, the Universe was still extremely hot. The potential of the false vacuum "rolled further down" and may be seen as a period
of particle creation, and symmetry breaking, where the different fundamental forces came to existence.

Note: while the Energy of the false Vacuum rolled down, various fields emerged, like for example notably the Higgs field,
which is a scalar field (present everywhere in space), responsible for "dragging" particles, or in other words, attaining mass to them.

It might be unbelievably, but we are still within the very first second of creation ! After about 1 μ second after the "Bang",
protons and electrons were formed. (Ofcourse, actually first some "quark epoch" should have preceded this).

Note: Now, we are skipping a number of phases. For example, the Standard model also assumes that matter and anti-matter was created.
These two types should annihilate each other. Somehow, a small amount of regular matter was preserved, due to some "skew", or "bias",
or insymmetry, that preserved some regular matter.
Also, how exactly "dark matter" fits in, is not yet very clear as well.


Note:
Two major scientists were involved in Inflation around the 80s.
The original Inflationary Theory was created by Alan Guth, around 1980. He was more oriented on the "in and outs" of Inflation itself.
In that same period (more or less) Andrei Linde came with similar ideas, but it's probably fair to say that inflation for him
was a helpfull tool to develop ideas about the "Multiverse" (multiple Universes).

2.3 Now what about those "ripples" or "curles"? (as shown in fig.2):

There exists quite a few 'Inflationary theories", which all differ in relevant details.
Some of them, do not predict gravitational waves at Inflation. So, if the curly polarization is due to
streched space, caused by gravitational waves, then those versions of Inflation are not right.

By the way, the current observations might impact other theories as well.

Some other Inflational theories, like the original one, do speak of gravitational waves.

A part of the original Inflation theory, with respect to Inflation, goes a bit like so:

At a certain point, we have this negative pressure of the false vacuum. Pressure looks a lot like "gravitation", so some folks say
we have a "repulsive, or positive, gravitational field", which actually drives inflation.
At a later stage, as the vacuum "rolls down", matter is created with a enormous energy. The gravitation field will compensate, and it gets
more and more negative to compensate.
At a certain point, gravitation start behaving like we are used to, and finally waves ripple through the primordial Universe.

The curly b-mode polarized thermal background radiation, thus might well be produced by those gravitational waves, which are stretching/bending space,
which is the real cause for those curly polarized components in the thermal background radiation.


Appendix: high-level overview of the Timeline of the Universe:

To conclude this simple note:
The following two (public domain) figures below, might give a reasonable idea of the "Timeline of The Universe".


Fig. 3. Timeline of the Universe.





Ok, that's it. Hope you liked it...