Probing the very early universe (part IV)


Catch up with the saga: part I, part II, part III

Negative Pressure, Exotic Particles, and the Emergence of Something out of Nothing

So, lets quickly recap. We have evidence that the Universe is expanding, and that the distribution of galaxies is both homogeneous (smooth) and isotropic (the same in all directions). What’s more, our theories of universal evolution tell us that the universe appears to be made up of 50,000 regions that are causally disconnected; they are independent. But since the universe is also homogeneous, this means that for some mystic reason these 50,000 regions managed to evolve in practically the same way as each other.

Physicists do not like mysticism and so they treated these phenomena as paradoxes, mysteries that need to be solved, and a neat solution was proposed in the late 70s/early 80s dubbed inflation. This is the very rapid expansion of the universe at early times, which allowed the universe to be much smaller than we thought it could be, and expanding to the size necessary to account for the subsequent evolution, without upsetting the status quo of the standard Big Bang theory. All this was discussed in part III of this series, and we left off at the point where we asked “How does inflation solve the origin of structure puzzle”, and we shall pick up there.

To be able to answer this question, we need to understand the process and nature of inflation a bit better. The equations that `govern’ or `describe’ the expansion of the universe are known as the acceleration (or Raychaudhari) equation, and the Friedman Equation. These equations relate the rate at which the universe is expanding to the content of the universe. So, if we know that the universe is composed mainly of radiation, the Friedman equation would then tell us the rate at which the universe is expanding, and the Raychaudhari equation would tell how that rate was changing.

acc

Combined these equations tell us that if we want the expansion to accelerate, as is necessary for inflation, then we need something which has negative pressure or negative energy. Since negative energy means negative mass that makes it too weird to make sense (even for cosmologists) so focus was placed on finding something with negative pressure.

Negative pressure:

So what is negative pressure? To get an intuitive understanding of this, imagine that you are blowing air into a glass bottle which cannot expand. As you blow into the bottle you are forcing the air molecules closer together, this is known as positive pressure. Negative pressure (you guessed it) is like sucking air out of the bottle, you are forcing the air molecules away from each other.

So negative pressure forces things away from each other, it acts like anti-gravity, which means that negative pressure could have caused the original expansion of the universe! So the question is what has negative pressure?

We know that everything we have encountered in the universe (be it in the form of matter or radiation) has normal positive pressure, so we really are looking for something as yet unencountered… something exotic.

Exotic particles:

I struggled with this bit. I wonder if people are aware of what is known as the particle-wave duality? Sometime in the 1800s Thomas Young showed that light behaved as a wave, it spreads out like ripples on a pond. In the late 1800s Thomson showed that light also behaves like a particle a.k.a a photon. Both theories are correct, light behaves as both a wave and a particle.

To get the universe to expand very very rapidly the average pressure must be negative, which means that you would need to fill it with a particle that pushes everything away from it. Such a particle has never been observed in nature (hence is exotic), but is a necessary component of fundemental theory, it is known as a scalar particle (wave) and in the context of inflation we call it the inflaton.

Initially introduced to solve the paradoxes of Big Bang cosmology, it was found that the inflaton has another trick up its sleeve … the ability to create the ‘wells’ into which matter will eventually fall and form structure (like galaxies). To achieve this we need to speak a bit of quantum field theory (dont stop reading I shall try to simplify this as best I can!).

The basic idea is that on very small length scales things don’t act normally … on a tiny level everything around us is fluctuating, an electric field may have a specific amplitude (power/strength/value) to the naken eye, but look close enough (hypothetically) this amplitude is changing, it is sometimes less and sometimes greater than the average value that we measure. This happens so rapidly however that you would never notice. Does this make sense? Check out the next figure …

In the classical view (i.e. visable to the naked eye) we would see the wave change with time. But invisible to us there are tiny fluctuations and if we magnigfied this we would get a picture like the one in the next figure.

Having magnified the circled region in the previous figure we see that our first impression of the wave was not complete. To get a better idea of what is going on you have to imagine that the classical wave is frozen and the small fluctuations are wiggling rapidly.

So if the fluctuations are wiggling rapidly, and dont have an effect, how can it lead to ‘fixed’ tangible wells into which matter will eventually fall into… read on.

The Quantum to Classical Transition (the Emergence of Something out of Nothing):

Remember that the universe is expanding extremely rapidly? Ok, well since the inflaton is also a wave, it stretches out across the universe  and gets stretched out or magnified by the rapid expansion. So pretty much as soon as a little wiggle appears on the background (the average value of the wave or the classical picture above) it gets blown up to ‘proper’ proportions. These ‘proper’ proportions are what we call classical, their value becomes fixed and the wiggle stops wiggling.

Since the wiggles can be any length when they get transformed to classical size we end up with a range of different sized peaks and troughs across the universe, and because they are classical they survive through the end  of inflation, and effectively determine the pattern of galaxies we see across the sky.

Questions?

Next up: how do we test this idea we call ‘inflation’?

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Probing the Very Early Universe (Part III)


Apologies for the delay in this post, I had started writing this ages ago, it was taking me forever to get the images right, and when I thought I was done, I lost both the post and the images!! I lost the will to live.

Catch up with the saga: part I, part II

A Neat Solution, Inflation

In the early 1980s, physicists started to take note of a theory that seemed to hold all the answers. The theory, cutely called ‘Inflation’ by MITs Alan Guth, offers a neat solutions to The Three Paradoxes of the Universe. In this post I will attempt to explain what inflation is, when it happened, and how it works.

What is Inflation?

Inflation is basically the very rapid expansion of the universe, where two points move away from each other at the speed of light(1). This does not contradict the special theory of relativity, since at the time this happened, the universe was classically empty, only energy existed at this time.

When did it happen?

Hard to quantify too precisely, but we can take on board two bits of information from two different sources in order to give a ball-park figure on this. Inflation must obey the physical laws of nature, there is no escape, however we are not entirely sure what these laws looked like such a long time ago.

[Extra Reading] The origin of the fundamental laws of physics:

One of the fundamental ideas of physics is that all the physical forces that we see as independent today (i.e. the force of gravity is seen as independent of say the theory of electromagnetism), were actually all ‘united’ many years ago, when the energy of the universe was ‘free’ (i.e. not bounded by structure, like atoms and such). That is, billions of years ago, physicists think only one law of nature existed, and that as the universe grew and cooled, this one law subdivided into a few sub-laws of nature. If you’re a bioligist or are more comfortable with the ideas of biology, think of this evolution as a top down process, as opposed to biology’s bottom up approach to evolution. So if a physicist had come up with a theory for the origin and diversity of the species she would have imagined one super-being (not divine, just super, as in ‘super duper’) that then spawned lots of other species, who then spawned even more species! But this spawning of mutants was already encoded in the first super-being, i.e. all the DNA any animal/plant needed existed within the chromosomes of that first super-being, and the genes ‘came to life’ as it were in response to the environment. That is the basic idea of the unification and subsequent diversification of the laws of physics, with the environment being the temperature/size of the universe.

Now, the physics world has managed to unite all the fundamental forces… except for one: Gravity. But that is not what we’re talking about, we assume that gravity did somehow unite with the other forces, and generally, gravity appears after what is known as the Planck epoch. The Planck epoch defines a time when the early universe was only a Planck length in diameter. This Planck length is special, in that it defines the smallest size that we know how to analyse physically i.e. we have a theory of how things behave when they are very small, or very very close together, but not if they measure less than or are closer than a Planck length. Since inflation deals with the expansion of space time, it needs general relativity (aka gravity) in order to operate, so Inflation takes place after the appearance of gravity.

So as a first guess Inflation takes place at least billion billion billion billionth of a second after the Big Bang. But to be brutally honest, since the theory of inflation is still work on progress, then inflationary cosmologists also look at scenarios when inflation took place at or before the Plank time, that is: less than 10 million billion billion billion billionth of a second after the Big Bang.

The second bit of information we need is when did the contents of the Universe become dominated by radiation? That occurred about a 10 millionth of a second after the Big Bang, and we need the universe to have ‘settled down’ by this time, because our theories of what happened after this time (the `standard’ Big Bang evolution) hold up pretty well under scrutiny, and we dont want to change things too much.

So inflation took place between a billion billion billion billionth of second after the big bang and 10 millionth of a second after the Big Bang. This would seem pretty precise for most people, but remember in the early universe aLOT of stuff could have happened within this time, after the universe became radiation dominated it took only 3 minutes for the temperature to drop 999,999,999,999,999,999,900,000,000 degrees Celsius. So we may have nailed the epoch of inflation to a few millionth of a second, but that still leaves alot of room for uncertainty.

 

How does it work? i.e. how does it solve the Three Paradoxes of Cosmology

How inflation explains the causality, homogeneity and isotropy of the universe?

inflation1

This is a schematic diagram of the expansion of the universe. The figure on the left represents the standard big bang expansion, assuming only radiation and matter. The figure on the right represents big bang + inflation. To understand this diagram, you need to imagine that our universe is contained within the black lines, and that it grows as you follow the arrows.

Looking at the figure I have included (click on it for a better view), I have attempted to illustrate how the two different scenarios (Standard Big Bang vs. Inflation and Big Bang) expand. You need to imagine that our universe is contained within the two vertical black lines, so it grows as you follow the arrows.  Now, what we know of the age of the universe, and what we know about how radiation and matter (regular stuff) effect the rate of expansion, then it turns out that there were 50,000 parts of the universe not in causal contact. That is, the universe could not have been small enough for these parts to communicate. That is, 14 billion(ish) years ago, according to standard lore, the universe was made up of 50,000 independent regions. So why did these regions all evolve in the same way?

This is where inflation comes in, because inflation stretches the universe out in such a tiny amount of time (see previous section), it means that the universe could have started out much smaller than was actually thought, and expanded very quickly, all this without effecting the evolution of the universe from light to atoms to galaxies to us (i.e. Big Bang Nucleosynthesis). Referring back to the figure, the red and blue circles represent two regions in the universe, in the inflationary picture they start off very close to each other, so information gets shared between them, or more to the point the universe mixes and homogenizes

How does it solve the problem of the age of the universe? (or why isn’t it older?)

Since inflation causes the universe to grow to the size required by the theories which govern Big Bang Nucleosynthesis in a teeny fraction of a second, our theory of universal evolution now accounts for the age of the universe. We no longer need to add to the age of the universe to account for phenomena.

How does it solve the origin of structure? (or where did all this stuff come from?)

The answer to this one is quite involved, we need to look at how one gets inflation, i.e. what causes the universe to expand so rapidly? Once we answer this question, we discover that inflation also explains the origin of structure AND why it started expanding in the first place.. for next time though 🙂

(1)this is one scenario, but the other one is too complicated to explain right now

Next up: Negative pressure, exotic particles, and the emergence of something out of nothing

Probing the Very Early History of the Universe (Part II)


Catch up:

Part I: The Big Bang Theory

What the Standard Big Bang Theory does Not Predict or Explain

In the previous post I outlined the basics of the big bang theory. As things stand, there remain a few issues which have not been addressed, and are taken as principles or ‘as given’. There are still many major mysteries of the state and origin of the universe, however for the purpose of this series, I will focus on three.

Paradox 1: the homogeneity and isotropy of the universe

The dictionary defines homogeneity and isotropy as follows:

Homogeneous:  Of the same kind of nature; consisting of similar parts, or of elements of the like nature

Isotropic: Having the same properties in all directions.

And these are the properties that the universe seem to exhibit. Namely, regardless of which direction you observe the properties of the universe, it appears the same. The standard Big Bang theory as described in the previous part offers no explanation to this phenomena.

Paradox 2: the age of the universe

To get an estimate on how old the universe is, cosmologists use a combination of astronomical observations and theory. One way of doing this is by observing distant clusters of galaxies, then plugging in the theory about how these clusters evolve, one then gets an estimate on the age of universe. The estimate is repeated with other structures, so the observers seems pretty sure of the estimate 13.7 billion years.

So far things are looking pretty consistent, we can estimate the age of the universe using theories of how galaxies and stars evolve, and also from the expansion of the universe. Since, if our understanding of the Big Bang and the expansion of the universe is correct we should be able to figure how long it has been doing so.

We hit a pretty big snag though when asking the question “how big was the universe when light ceased to be trapped by electrons?”. The answer naturally is “much smaller than it is today”, which is fine, except for one thing, it was not small enough to explain the why the universe was homogeneous and isotropic.

I’ll explain, remember that the universe is expanding, so when we look up into the night sky, two points in the sky that are today very far apart, would have been very close together in the past. Remember that the universe is homogeneous, now I am going to try an analogy (and am rather naff at them) take a water tank with a divider down the middle, pour water into one side and sit back. The system is now in-homogeneous, one side has water the other does not. How do you get water from one side to the other (each side has an individual lid and they are sealed), obviously remove the divider, now water flows into the second chamber and we have a homogeneous system! What did you do? You allowed the two chambers to communicate (exchange water and air), the divder was blocking information (water and air).

In the universe, distance is the barrier to exchanging information (in this case light), since light can only travel a certain distance in a certain time. So back to our problem, about 310,000 years after the big bang, the universe was quite big so a point in that universe could not have communicated with all other points. On top of that, rewinding 300,000 years, using known theories, the universe still wasn’t small enough, and a point still could not communicate with all the points in the universe!

So the question is: how did the universe end up homogeneous if one half of it didnt know what the other was planning? Coincidence?

Paradox 3: the origin of large scale structure (aka galaxies and galaxy clusters)

Phew, that last effect I find the hardest to explain, this one is relatively simpler (she says). In the Big Bang theory one needs an original ‘mass’ in the various places in the universe where we see galaxies and stuff today, this local fluctuation in the uniform mass of the universe will then attract more matter towards it and grow and grow till the galaxies and stuff appear. The Big Bang theory just ‘assumes’ it exists.

Told you it was simple 🙂

Now what we need is an explanation, a phenomena, an IDEA! We want this idea to explain how the universe is so uniform, why it is uniform, and how come we end up with these ‘mass fluctuation’! An we do, it’s called ‘Inflation’…

Part III: a neat solution, Inflation

Probing the Very Early History of the Universe (Part I)


I may be giving a public lecture on this topic in the near future, and this will be the first such lecture I would have given. Therefore I shall practice on my few readers, and try and present my research in laymen terms. Please feel free to question me and highlight any areas that I have not been clear in or issues that need further elaboration.

I shall start this series with an overview of the origins and content of the Big bang theory.

The Big Bang Theory

Einsteins theory of gravitation

Gravitation is the force that attracts masses (bodies) to each other. The Newtonian view (i.e. according to Isaac Newton) was that gravitation was like an invisible force field connecting bodies to each other, the strength of this force increased in proportion to mass and decreased in proportion to the distance between the bodies. This idea was revolutionized by Albert Einstein. He made the connection between the mass of the body and the geometry of space. Basically a mass would distort space, effectively creating a dent in space, so when another body passed by, its path would be affected by this distortion.

To get a better idea of this phenomenon, imagine a rubber sheet nailed at its corners to a square frame, now run a small ball across this sheet and it will follow a straight path (ignore friction). Now, in the middle of the sheet place a large heavy ball, you will note that the sheet dents with the centre of the dent where the large ball is. Flick a smaller ball tangentially to the dent and it will spiral around the ball, flick it towards the large ball and it will fall towards the larger ball following a curved path. In this analogy the rubber sheet is space, and it is in this manner that gravitation works.

Point 1: masses distort the geometry of space.

Einsteins original theory predicted that space should be expanding, but this was in contradiction to the theory at the time that the universe was static. As a result of this Einstein added a term to his equation to counteract their prediction of an expanding space.

Point 2: Einsteins theory predicted an expanding universe, but he modified them so that they predicted a static universe.

Hubbles paradigm changing discovery:

Not long after Einsteins inception of his theory of gravity, the astronomer Edwin Hubble made a paradigm changing discovery. He rather accurately measured the doppler shift of neighboring galaxies.

Doppler shift: when a car is moving towards you the sound of the engine appears to be increasing in frequency, and when it is moving away from you the sound appears to be decreasing in frequency. This phenomenom also applies to light. Light can be viewed as a wave, and when the source of the light of moving towards you the frequency appears to increase and vice versa. A lower frequency corresponds to the infrared end of the light spectrum (see figure) and a higher frequency corresponds to the ultraviolet (or blue) end.

visiblelightspectrum2

The spectrum of light. The blue end has a higher frequency (smaller wavelength) than the red end

Anyway, Hubble discovered that on average, the galaxies exhibited a red shift and that the further a galaxy was away from us the faster it was moving away. In other words he discovered that the universe was expanding. Well, Einstein was left a bit red faced following this discovery. Friedmann and Lemaitre then independently derived the Friedman Lemaitre equations from Einsteins equations showing that the Universe is expanding.

Point 3: the universe is expanding.

Point 4: Einstein was embarrassed, and reverted to his original equations. 

The Cosmological Principle and the Inception of the Big Bang theory

The Cosmological Principle states that on large scales the universe is both homogeneous and istoropic. In simple terms that means that in general, the properties of the universe are the same regardless of the direction of observation. This principle are apparent in Lemaitres equations, which showed that the universe was also expanding.

Lemaitre took this property of a future expanding universe one step further, and predicted that the universe was smaller in the past. This can be extrapolated to a point in the past when the volume of the universe was zero, this is known as the big bang singularity.

So what does the big bang theory tell us?

Well, there is a relationship between the size and temperature of the universe, namely as the universe expands it also cools. So the early universe was very hot, so hot in fact that matter would have not existed. Instead the universe was radiation dominated, it was a gloop of photons (particles of light) and highly energised subatomic particles. In this gloop particles and their nemesis the anti-particles would collide with such energy that they gave off radiation in the form of gamma rays which in turn decayed to form the particle-anti particle pairs. This state of affairs could not be supported as the universe cools, and eventually the annihilation of particles with their anti particles ceased to occur.

At this stage higher forms of matter could be sustained, i.e. electrons, protons, neutrons. The density was still quite high though, and photons were often deflected off electrons (known as Thompson scattering) and therefore a photon could not travel very far before it bounced off an electron. The free path of the photon was short, and the universe was effectivley opaque to light.

The universe was adament in its expansion though, and eventually the density of matter dropped so that light could travel freely without hindrance. The electrons had anyway combined with the protons and neutrons to form neutral hydrogen rendering them practically harmless to photons. This time, when the photons are released from their Thompson prison is known as matter radiation equality.

The freed light, this relic of the early history of the universe, is known as the Cosmic Background Radiation, and permeates the universe till today. The properties of this radiation/light can be accuratley estimated using the black body analogy and it was calculated that the Cosmic Background Radiation would have a temperature today of 2.74 Kelvin (about -270.3 Celcius) , this was first measured by Penzias and Wilson in the 1960s.

The theory also offers a neat chronology of events to how stars and elementary chemicals are produced, but this part can be neglected for the purpose of this presentation, since we are primarily concerned with the very early history of the universe.

Next: what the big bang theory does not predict

 

The Muhammed Institute for Science of the Cosmos


Cosmology may be coming to an institution near you. The Middle East is surprisingly uninterested in cosmology, even though we have at least one eminent cosmologist that I know of (Qaisar Shafii from Egypt), cosmology has failed to take root in the academic institutions in the region. This I always found surprising, for research into theoretical cosmology is cheap to fund, all we need is a computer with an internet connection, and a supply of paper, pencils and erasers. I also find that arabs are very curious about cosmology, most arabs I meet quizz me about the Big Bang theory, the origins of the universe and such. Stephen Hawking was met with a huge crowd when he visited the university of Birzeit in 2006, yet the Centre for Excellence in Theoretical Physics and Applied Mathematics due to be built with EU funds sometime in the future do not have cosmology on their list of research aims (in fairness though they were very open to the idea of possibly including it). Apparently attempts to establish cosmology research groups in Lebanon, Egypt and Morroco have failed, due to apathy, and lack of a conducive research environment. This was a wakeup call to me, I had always thought that moving back to the Middle East and establishing such research would be a doddle. I do find it surprising on another level, since the Middle East is predominantly Muslim (except Lebanon, but even there we make up 50% of the population!), and the Quran strongly urges “looking up at the stars and pondering their origins” (c.f. Aal Imraan verse 191 + many more).

As a result of these unpromising experiences Dr Al Fakir has established the Muhammed Institute for Science of the Cosmos (MISC) and they have just launched their website.

WHAT THE MISC DOES
The end product of MISC operations are substantial advances in astrophysics, cosmology, and space exploration, in the form of scientific papers in internationally recognised refereed journals, and collaborative experimental projects. To that end, MISC activities include (1) organising annual conferences brining together the MISC research community at large, (2) supporting specific research collaborations between groups of MISC researchers, (3) supporting senior researchers in dedicating extended stretches of time to the MISC, (4) planning and promoting Earth-based and space-born experiments that have bearing either on the physics of the Universe (gravitation, microwave background, etc) or on the origin of life (solar system exobiology, astrobiology, etc), (5) creating and nurturing branches of the MISC in various parts of the Muslim world, (6) creating opportunities for promising young researchers from the Muslim world to collaborate with seasoned MISC researchers.

Of particular interest is the list of eminent non-muslim cosmologists who support the institute, Alexander Vilenkin, Robert Wald and William Unruh, which I find extremely promising. Eventually they plan on being able to fund visits to institutions in the Muslim world with a resident cosmologist, or visits from cosmologists based in the Muslim world, with the possibility of funding postdoctoral and permanent staff members. The potential increase in job opportunities aside (something of extreme interest to someone at my level), this will be great for the middle east (and muslim world as a whole) on many levels. It will foster creativity and ‘outside the box thinkin’, something I find to be lacking in the arab countries at least, interaction with experienced cosmologists, and the potential in excelling in something other than conflict and commerce (as in the UAE). The Muslim world has a strong history in Astronomy (see 1001 Muslim Inventions and George Saliba’s site for a summary), that even though we managed to severley neglect, makes us naturally disposed to this branch of science and we really should foster it once more.

more on the expansion of the universe…


Hubble only observed around 46 galaxies. His experiment has been redone with more advanced telescopes, including the space-based hubble telescope.

Again you (qwaider) have hit upon a good point in saying that the data may be deceptive… in science we can never declare a theory ‘proven’ we can only declare it to have ‘strong supporting evidence’, and the more tests there exist for a theory the stronger the evidence becomes.

The expansion of the universe is not only based on the observation of galaxies and their redshift. A consequence of universal expansion is the Big Bang, a consequence of  that is that the universe must be filled with radiation with an average temperature of 2.7K. A measurement of that is in fact is an indirect measure that the conclusion of an expanding universe is probably correct.

Now, the radiation was detected in 1965, and it was found to be homogeneous and isotropic across the sky. This means that no matter where u pointed ur telescope in the sky u would measure 2.7K. This would not be possible unless the origins of the universe were homogeneous across the sky, and also the universe today. This means, observing galaxies in one region of the sky would produce practically the same results as observing galaxies in another region (pretty neat I think).

Again, a precise measurement of this radiation has been made by space based missions (which can detect varations on the micro-kelvin limit) confirm that the average temperature of the radiation regardless of where in the sky is uniform. Check NASA’s WMAP site for more details on this type of mission.

The WMAP sattellite though also measures the light detected by galaxies, so again a confirmation of results done by Hubble type survey’s.

In conclusion, the expanding universe has VERY strong supporting evidence 🙂

hope I have convinced readers… I will get onto the questions on the Big Bang later.

In response to Qwaider: the expansion of the Universe etc.


“I’m a little bit skeptic of expanding, static, contracting, ever expanding, accelerating expanding universe being finalized at any point. For all we know, the universe is moving, but might not necessarily be expanding. Maybe particles are moving in all directions like water in a balloon, and that we haven’t examined all possibilities yet.”

To determine the evolutionary state of the universe (expanding-contracting-static) one uses the doppler effect. Simply put the light from an object moving away from us is red shiften whereasthe light from and object moving towards us is blue shifted. So basically what is done, is that the doppler shift of distant objects is measured, and overall was found to be red shifted. i.e. on cosmological scales, the universe is expanding.

“And I don’t think relating that directly to a Quranic verse is a wise idea.”

i do agree to some degree. When performing reseacrh, ideally one should have no expectations… that is the only way one can generate unbiased (by default: reliable) results. I dont think that people active in scientific research should go around making comparisons between their science and their religion… if it is done, it is best done by someone who has studied both the science and the religion… thus will be taking the unbiased results of the scientists and seeing how they compare to the religion… otherwise you may end up committing the same mistake as Einstein… who altered his equations based on his preconceptions of the univers ;).

The expansion of the universe has been established, and was later found to be in the Quran, I figured it was a safe example to use.