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By Prof. G. Venkataraman

Previous Articles In The Same Series

Universal Cycles

Loving Sai Ram and greetings from Prashanti Nilayam. I hope you remember where we cut off last time. Just to refresh your memory, I brought you up to the point where I gave you a very rough outline of the Ekpyrotic Model of the Universe. In this model, the Universe has a cyclic existence, somewhat like what I described earlier with one major difference, which is that in this case, it is the repeated collision of two adjacent branes that leads to the repeated birth of the Universe. Last time, I merely gave a very rough outline, leaving the details for the next instalment; that is where I shall pick up from, this time.

Let me start with the following sketch that compares the Inflationary Model [where one does have any question of the Universe being born again and again], and the essentials of the Cyclic Model.

Quest for Infinity

FIGURE 1: This figure, adapted from the book of Paul Steinhardt and Neil Turok, shows side by side, the sequence of events in the Inflation Model [based on the work of Alan Guth] on the one hand and the Cyclic Model on the other [based on the work of Paul and Neil]. The essential difference is that in the former, once dark energy takes over, the Universe keeps on expanding till eternity. In the Cyclic Model, however, a contraction process takes over from dark energy on account of energy considerations. This would become clearer later in the article. For, now, the two sketches above may be regarded as the “statements” of the two “camps”.

Notice, that where the Cyclic Model is concerned, there are certain physical processes that repeat over and over again, cycle after cycle. The processes mentioned are nothing new, and bits and pieces of this scenario have been mentioned earlier [like radiation domination, dark energy dominating, etc.] all of which, by the way, feature in the Inflationary Model also. There is, however, one significant difference and I am sure you would have noticed it; which is that in the Cyclic Model, there is a contraction process that comes into play towards the end, after expansion has had its full say; this contraction is of course absent in the purely Inflationary Model. What is left for me to do now is place all the different steps of the Cyclic Model within the framework of what Paul Steinhardt and Neil Turok refer to as Ekpyrotic Model. Not an easy task, but let me give a try anyway!

Describing the Ekpyrotic Model

It all boils down to describing what happens at three levels so to speak. Level 1 would be all about the separation between the two participating branes, which, through periodic collision, are responsible for the Cosmic Dance of the Branes, leading to a Cyclic Model of the Universe. In level 2, I would have to focus on what happens in the brane which carries our Universe. Then there is level 3, wherein I shall try and link the changes occurring during the evolutionary process to the energetics of the process; this is like describing what is happening in the engine of a car, as the car is travelling on a road that goes up and down and has many curves. That pitch, I hope, would have you tuned to hearing now the amazing story of the Dance of the Branes, and repeated incarnation of the Universe.

I shall present this narrative using a figure that appears below. This figure has three parts, related respectively to the various “levels” that I just referred to.

FIGURE 2: This figure has three parts, related to the three levels mentioned above. In (a) is shown a schematic depiction of one complete cycle according to Paul and Neil; this sketch is based on an illustration in their book. The sketch in (b) is a repetition of Figure 1, but tuned to that in (a). The sketch in (c) has two parts; in the first we have 2 (b) shown with dots in a sequence. The other part of (c) relates the states 1, 2, 3, etc., to the energetics of the brane-pair. The latter aspect is important and would receive mention again later.

Let me now explain slowly what the above figure portrays. The best way of doing that would be to give a “blow-by-blow” running commentary, starting with the point marked “YOU ARE NOW HERE”. By way of adding some fun, maybe I shall call upon the famous Sanjaya of Mahabharatha fame to do the commentary [broadcast to the innumerable Universes created by God!]

Sanjaya on the ‘Dance of the Branes’

Hello folks! This is your ethereal Sanjaya, reporting to you in this Kali Era and bringing to you a never before presented drama, the Cosmic Drama of the Branes ordained by the Lord. The scenes you are now about to witness, are not only breathtaking and staggering but may also be frightening; so we advise that if there are kids around, they be given some candy and sent out to play. Make sure you keep them out till this show is over. Maybe they can see a DVD of this Cosmic spectacle, when they grow up; but right now, it may be a bit too much for them!

Well, what do you know? I thought my job was over when I reported live on the Mahabharatha War, but here I am again, doing yet another live commentary. This is a very different kind of job, for I am not in the world nor even in the Universe, where you are, watching all this on your nice plasma screen. I am out there – I don’t know what to call it for this cannot be the space you folks talk about. This is outside the Universe I once was in, and also its companion Universe, about which you are going to soon hear a lot. I am far away from these branes on the collision path, hanging out I do not know where, maybe some kind of a Trishanku (the middleground according to mythology which is neither earth nor the sky and is somewhere in between)!

Anyway, get set for a new spectacular show, a never-before-in-motion-picture-industry job, far, far superior to any Hollywood or Bollywood block buster; and the strange thing is we are going to keep you at the edge of your seat without any of the usual heroes or gangsters, and the standard chase scenes, gunfights, and what not. In fact, you will not see a single human, or for that matter, even an ant. Indeed, this block-buster is for real and far superior to any Star Trek type movie you could think of!

Enough of this prattle, for the Cosmic Director has just given the command ACTION and so here I go!

The opening scene. I see two branes, separated by a small distance, a part of the third dimension. In a sense, it is ridiculous to call it the third dimension – it is so small in length; yet, it has been declared to be a dimension by the script writers Paul and Neil, and so I shall stick to that terminology.

Quest for Infinity
Dark matter increases expansion of the universe, spreading out galaxies and matter

So there you have these two branes, about one mm or one cm apart, I cannot really say exactly how much. But the separation is not really the important part of the story. As I look at what appears before me, I see two brane Universes, sort of wrinkled somewhat. One of these, the one on the right I believe, is the Universe where planet Earth exists.

Glancing quickly at my notes, I can say we are looking at the Universes at the moment when dark energy is taking over and beginning to call the shots. If you recall, dark energy is a kind of negative gravity force, a force that causes repulsion rather than attraction. Thus, dark energy leads to expansion instead of contraction; that is the point you have to bear in mind.

Trillions of Years Go By…

There is a fast forward now, and we have moved ahead, oh maybe a trillion years. And what do I see? I see the same two brane Universes. They have not moved much in terms of their positions or separation. But something has changed; and that is the brane sheets are now flatter, with fewer wrinkles. Also, the two Universes have expanded a lot – remember that it is dark energy which is now in charge. And thanks to the expansion that I just mentioned, matter density is very small.

Quest for Infinity
Dark matter predominates, evaporating matter and radiation and the brane sheets become smooth and flat

We move forward some more in time, and now the branes are pretty flat and have zero matter you might say; also no radiation to speak of. This is the sort of pristine situation that forms the precursor for brane collision and the birth of a new Universe. So are we heading to something exciting? Let us wait and watch.

Some more fast forwarding, and what do I see now? Looks like something is beginning to happen; let me try and get a close look. Oh yes, it appears as if the dark energy has had its say, and something else is coming into play. Hey wait a minute! I see the branes start to come closer together! Does it mean that the spring like force that binds the branes has got switched on? It would seem so, which means that the state of the brane pair has started moving along the energy curve. You can see what I mean by taking a look at the inset on your screen. You see it? You follow what is happening, don’t you?

Quest for Infinity
Dark matter now evaporates while the spring-like force of attraction between the
two branes draws them close together

The Branes Dance Ever Closer

Don’t move, for things are going to get pretty exciting soon. And yes, sure enough, things have begun to happen, new things I might add. I can see the branes beginning to move closer and closer and even as they are doing so, wrinkles are beginning to appear on the branes. My notes tell me that these wrinkles are due to quantum fluctuations. Frankly I do not understand what that means; I mean when I cannot even understand what stock market fluctuations mean, how can I understand all this complicated stuff? Like I do, just pretend you understand what quantum fluctuations stand for, and let us wait and see if there are going to be any fireworks.

Quest for Infinity
As the branes come closer, quantum fluctuations cause their smooth surface to wrinkle

I have just been handed a note giving me some tips about what these quantum fluctuations are, and why they are important, and how they would influence the birth of the new Universe as also its subsequent developments. Apparently, the Good Lord knows – He knows everything does He not? – that if the new born Universe is super smooth, then it would be difficult to get gas clouds going; and I guess you are aware that without the gas clouds shrinking and all that, one cannot have stars; and where would planets be without stars? And where would humans be, without planet Earth? So, keeping all this in mind, the Lord has apparently ordained that even before the Universe is born, He would build in “special genes” that would facilitate the formation of galaxies, etc. Yes, it is all a part of the Supreme Master’s Master Plan, shall I say? See how thoughtful He is and so very compassionate? See how well He prepares and organises everything so much in advance?! And yet, amazingly, humans are so ready to forget Him, preferring video games, stupid TV shows, and so on! Anyway, that is a different matter altogether and let me get on with my reporting.

The Consequences of Temperature Fluxes

Quest for Infinity
Quantum rippling becomes intense causing temperature fluctuations

Folks, hold on! Looks like things are beginning to happen a bit more rapidly right now. The quantum ripples are all over the place; they are neither big in size nor in depth. I would say the biggest ripple is just about a couple of metres across and may be 50 cm in depth? Can’t see quite clearly from out here, but that roughly is what I would estimate the size as. I think this means that when the two branes actually hit each other, the so-called contact may not occur uniformly all across the brane; the contact may be earlier in some spots and later at others. Remember, when contact occurs, there is a Cosmic Fire meaning the temperature is going to shoot up – a few million degrees may be. But right now, the exact rise in temperature is not important. What is more important is that though the contacts across the plane of the branes may take place at slightly different times, which might be different only to the extent of who knows, about 10-25 seconds. However, that miniscule difference is enough to make regions hotter than others.

You get the total picture, don’t you? The two branes are approaching each other; this approach is due to gravity pull. The branes are flat to start with but develop quantum ripples when they are about to collide. As a result of the ripples, the contact between the branes does not occur simultaneously all across the branes but at slightly different times at different spots. Thus, while the collision does produce a Cosmic Inferno, the temperature across the branes is not quite the same at different places; they differ slightly, and it is this slight temperature variation that later would act as a great incentive for galaxies to form in some places and not in others.

A New Universe is Born

As I speak, what do I see? Oh my God! I see a huge inferno, and I simply cannot describe it!! The last time I saw such a spectacle was when the Good Lord as Krishna revealed His Cosmic Form to Arjuna, and at that time I said it was brighter than a thousand Suns! That was a gross understatement; the Cosmic Inferno I now see before me is brighter than countless Suns; it is Infinity itself! Imagine that, actually seeing the birth of a new Universe!

Quest for Infinity
Wrinkled branes collide unevenly, causing non-uniform distribution of hot plasma

But Where is God?

But there is something missing, and I have just realised what that is. A new Universe is being created, out of a Cosmic Fire of immense and Mind-boggling proportions; but where is the Lord? Where is He hiding Himself? Where is He? Don’t understand that at all! Is He hiding Himself as He often does, so that we might be seized with eternal doubts as to whether He exists or not? Is this one of His inscrutable Leelas?

Hold on folks! I have just been handed a slip from our news desk that monitors the wire services. It says, according to a report by Sage Narada, the Lord was sighted in a country called India and He was last seen at a place called Puttaparthi; the report also says that it looks like the Lord is likely to temporarily shift to some other place – I can’t quite read what is scribbled here; oh I can see one of those words it says Bangalore or is it Bengaluru? I cannot make out which. But I see another word also; can’t quite pronounce it – but I shall spell it out for you; it goes like this: K, O, D, A, I, K, A, N, A, L! Well, there it is, the latest rumour about the Lord’s physical whereabouts. I really do not know where He is but I do recall His telling Arjuna, “Oh Arjuna, do not look for Me here and there; if you really want to find Me, search in your Heart.” That being the case, I wonder why humans are having a problem finding the Lord; maybe a lot of heart problems out there!

Anyway, let me get on; sorry for that interruption. Things are really beginning to happen out there in the strange world of Cosmic Branes, trying to create Universes through collision. Earlier I told you about the two branes, rushing towards each other, not super smooth as they once were, but with tiny quantum wrinkles – could they be called Cosmic pimples? Maybe I had better not! This is God’s Drama and I had better watch out and be careful about the words I use!

I then told you about the collision, temperature rise and all that, when I started digressing about Krishna . That collision was over in a flash. Technically, however, because of the wrinkles, different regions of the branes made contacts at different times. These time differences were extremely small but large enough to cause temperature ripples, and these temperature ripples, I told you were the genes that later produced galaxies. Let me now pick up from there.

The First Moments of the Baby Universe

Well the first thing that happened after the collision was that the two branes were bouncing back, like a recoil from collision. Interesting point here – the branes were rebounding with practically the same speed with which they collided. Imagine two billiard balls colliding head on, each with a particular speed. After the collision, you would expect them to rebound; that exactly is what happened here. Of course, if you think of two cars colliding head on, you would not expect this, would you? But then, this is God’s Drama and He has His own rules and grammar!

I have an expert here in the commentary box, Dr. Robert Super Brilliant, and let me shoot a few questions to him. By the way, last time when Krishna staged a Cosmic Extravaganza, it was a purely Spiritual affair, and therefore I had no need for an expert, technical commentator, all that padding to my prosaic narration to Dhritarashtra was done later by Sage Vyasa, who dictated a very detailed account of the entire proceedings to Lord Ganesha. Now, it is all different! A Cosmic Telecast, that describes the birth of the Universe in which Avatars incarnate, and this telecast goes out to all the other Universes where maybe it is the Devas who are watching. Mercifully, there are no commercial breaks; that is an abomination that only humans can invent! Anyway, here is Bob and let me turn to him.

A Super Scientist Explains

‘Hi Bob, how are you!’

‘Fine Sanjaya, nice commentary and congratulations. Will all this be available later as a podcast?’

‘Thanks Bob for your kind words; about the podcast, I don’t know, but I guess there must be some announcement in our website. But anyway, let us get to the point, and here I must say that I am thankful that you are here to hold my hands and help me through the sticky and technical aspects of what we are witnessing.’

‘Happy to help you Sanjaya, but I too have a problem.’

‘You, the Super Whiz Kid, have a problem? Can’t believe it!’

‘Sanjay, normally I speak only to my tribe and we folks simply wave hands, yell at each other and settle matter by writing complicated equations and arguing about them. I cannot do any of that, and I really do not know how to reach out to your audience out there!’

‘Well, I can see, you too have a problem, but it does not matter; just kick off and maybe we two would hold hands and come out safely!’

‘OK, go ahead, and ask what is it that you wanted to.’

‘Good, now tell me something about this rebound, why it happens, and how it plays out?’

‘I’ll give it all a try. You know Sanjay, it all starts somewhat like in a billiard ball collision. The branes collide and then they rebound. However, branes are not billiard balls, and being very different and with amazing properties of their own, there are many things different when you follow the post-collision scenario.’

‘Such as?’

‘Well, for one thing, the collision is so violent that the temperature produced is very high, like 1023 degrees.’

‘Wow! That is so high I cannot even imagine it!!’

‘No wonder, remember, this is God’s fireworks! Thanks to the astronomical temperature produced, there is a huge spray of particles and radiation, which fill both branes. This cocktail of particles and radiation is called a plasma – it is like a gas but instead of neutral atoms and molecules that we normally have in a gas, in a plasma we have charged particles. And it is this plasma that has such a high temperature. Now here comes a technical point.’

Quest for Infinity
Colliding branes rebound instantly, as hot plasma and radiation fills them

‘What is that?’

‘Frankly I do not know how to describe it – it is quite complicated really – but I can tell you what happens as a result.’

‘Which is?’

‘It is simply that the two branes fly away from each other after collision pretty fast, and when I say fast it means real fast. It is all over in an extremely short interval of time. That is to say, almost immediately after the collision, the two branes are where they were when they slowly started coming towards each other, about 1 mm or 1 cm apart, I cannot say exactly what the figure is.’

‘Wow! Now let me see if I have got it right. There they are, the two branes, all ready to move towards each to collide. They move slowly first and then accelerate, develop small quantum wrinkles along the line and finally collide. That produces real fireworks, and in the twinkling of an eye it is all over, with the branes back almost where they started from for the collision run – have I got right?’

‘Boy, you have done a terrific job! That would have done Carl Sagan proud! Let me continue and tell you what happens next. Even as the branes get back to their standard separation, the remnants of the collision, namely, particles and radiation, are filling up the branes. Radiation dominates but as the branes stretch, the radiation starts diluting. Matter does not spread out so fast and so in course of time, radiation dilutes away and we have a brane that is matter dominated.’

‘I guess that is when galaxies start forming, right?’

‘On the dot, and congratulations Sanjay for catching on so fast!’

‘Thank you; being with you has got me so excited, maybe I am learning without being aware of it! Please continue.’

‘Sure, will; now where was I? Oh yes, I was telling you something about what happens immediately after the two branes collide. We could describe this collision as a Big Bang, because after this collision, the Universe is born again.’

‘Hold on Bob; do you think that when this new Universe is born, it would have any excess baggage from the earlier birth?’

‘Oh, you are thinking of Karma, are you?! Well, in this case, according the authors of this new Ekpyrotic model, there should be none.’


‘Because, during the last phases of the previous cycle, when dark energy dominates and the Universe stretches on and on, matter and radiation get diluted to almost vanishing density. It is only at that stage the contraction starts, leading first to small quantum ripples and then the collision, which, the historian for this new Universe would describe as the Big Bang. Actually, this particular Bang would be one of a series of Big Bangs, coming one after another.’

Quest for Infinity
Radiation dilutes, causing matter to cluster around non-uniformities to form protogalaxies and eventually stars

‘Bob, you know what? As I look around, I see the quantum ripples getting amplified and blossoming into galaxies. In the Inflationary Model, the ripples came after the Big Bang, and formed due to inflation. But when branes dance, it seems the seeds are sown even before the collision occurs and the Bang takes place.’

‘That is exactly right, Sanjay. In the old inflation model, the quantum fluctuations were registered during the inflation, which occurred after the Big Bang. In the present scenario, there is no inflation; nevertheless, we do have quantum ripples and galaxy formation; the only difference is that the ripples form before the Big Bang and hang around afterwards too. I guess they are too small to get wiped out and manage to survive. And having survived and come thorough into a new era, they now play their assigned role – so it would appear.’

‘Very true Bob, and all that the Universe is supposed to do according to the Inflationary Model is happening right now via brane collision.’

‘Indeed Sanjay, but there are important differences and we must keep track of that.’

‘What are these differences Bob?’

‘Here they are - Difference 1: In the earlier scenario, we had one Universe that was born in a Big Bang, inflated like crazy in an incredibly short time, and thereafter lazily expanded, never ceasing to grow fat; this Cosmic obesity came not as the result of hamburgers but dark energy!’

‘Ha, ha, that is a good one!’

‘Continuing with what I was saying, in the present scenario, there is no inflation but repeated births. And that brings in Difference 2: The opportunity for repeated births means that time stretches legitimately even before the Big Bang, and so, the expansion rates, sizes, etc., can be adjusted such that one avoids inflation.’

‘Hey, wait a minute! There is something I do not quite understand. If what you are saying is right, it means that the Universe could have started with an “empty shell” shall I say at the time of the Big Bang, and thus had a finite size? In that case, all the earlier controversy about packing infinite energy into a geometrical point, having to do deal with a nasty singularity etc., - all those difficulties get swept away?’

‘Yes, it would seem so!’

‘And once the galaxies form, the routine is more or less as in the earlier birth?’

‘Pretty much so, I guess.’

The purists much among you might object to the above “stunt presentation”, bringing in a running commentary, consulting an “expert” and all that! I am sorry if I have offended your finer sensibilities, but my aim was just to take you through some difficult territory in as simple a manner as possible.

Just to make sure that you have got the gist of all that imaginary conversation between Sanjay and Bob right, let me present it in the form of the figure below. Here, you see all that was said above and earlier too, as a linear timeline. I trust, this figure would clear residual doubts if any.

Quest for Infinity
Quest for Infinity

FIGURE 3: Some of the sketches presented earlier are repeated here as a linear timeline to help understand the process better. In (a) are depicted eight states of the brane-pair, as they move forward and backwards, colliding in between to create a new Universe. This is the sequence for one cycle. In (b), we have the energy of the brane-pair in Fig. 2 (c) plotted as a “time stretch” extending indefinitely over many cycles. The dots in this figure relate to the eight states depicted in (a). It is important to note that the time stretch is highly non-linear. Thus the time span (ii) maybe a hundred billion times the time span (i).

It is important to appreciate that by building a spring-like mechanism into their model, Paul and Neil are able to over ride the dominance of the dark energy after a while and let contraction take over. It is this take over that then brings the branes close to each other and leads to collision, following which there is yet another Big Bang and a [re-]birth of the Universe.

At this stage, the question would inevitably arise: “How much of this model-making is supported by actual detailed calculations, computer simulations, etc.? Is this all a one big spin, or is there some basis for it? And, as one always asks in Physics, can one think of experiments via which this Ekpyrotic Model and the older Inflationary Model that could be pitted against each other, and we can check out which of the two options Nature has actually chosen?

Those are topics reserved for the next instalment! Till then, all the best and may God be with you always!

Jai Sai Ram.



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Vol 6 Issue 06 - JUNE 2008
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