Big bang in an infinite universe?

[I originally wrote this post for the UiS Cosmology Facebook page .]

Observations, in light of the standard cosmological model, seem to strongly suggest that the Universe as we know it today started in a point-like event some good 13 billion years ago. Since then it has grown and grown, and now we observe living in a flat (at least quite flat…) Universe. Thus it seems as if the Universe currently has infinite spatial extension! But is a point-like big bang event within finite past really reconcilable with the present state of infinite spatial extension? W. Rindler discusses this in a paper with the catching title “Finite foliations of open FRW universes and the point-like big bang” [1] published in year 2000. The solution is not simple (so we won’t work out any details!), but yet the mathematics is clear.

The clue lies in the space of simultaneity and choice of reference frames. By using the “Milne model” Rindler shows that the simultaneity space of an observer in one set of coordinates has infinite spatial extension, whereas the spatial section of simultaneity in another set of coordinates (co-moving coordinates) has finite spatial sections of simultaneity. Thus it is actually possible, concludes Rindler, that we now live in a universe whose space of simultaneity is infinite — yet it all came from the same point in finite past.

Note that this “point” where the universe originated is in itself not a trivial concept, since spacetime itself had –for all what we know — no extension beyond this point. Think of the surface of a balloon that starts off very small. The surface of the balloon is analogous to our world (our world is 3-dimensional though…). After the big bang (“big blow” in this case!), the balloon is much bigger. Note that the big blow event did not happen anywhere on the current surface of the ballon. It cannot have, since the ballon has expanded away from the “point” where the big blow took place. But if the big bang was truly a point-event — then one could also say that it happened everywhere (all the points on the current surface of the balloon came from the same super-small balloon in the past). So! One needs to be precise about what one means when discussing the singularities of space-time theories.

The bottom line is that yes: a big-bang event in finite past is in principle reconcilable with an open universe model!


What to do after the oil…

In todays world the focus on environmentally friendly energy sources is ever increasing. Perhaps Penrose’s idea from the seventies must be used… I originally wrote the below post for the Facebook page “UiS Cosmology” (

In 1971 Penrose and Floyd published a paper suggesting a mechanism to extract energy from a black hole. In their paper [1] they motivate their study from an analogous mechanism in the theory of pulsars (discovered in 1967), which are rotating neutron stars emitting energy in the form of radiation. These rotating stars have an enormous magnetic field (about a billion times as strong as that of the earth!) attached to it. Not only would compasses work outside the star, but one could extract energy from these fields. Penrose and Floyd now wanted to see if it was possible to extract energy from a rotating black hole! A black hole is extremely massive, so one could potentially expect this to be a huge battery of energy. Their hope wasn’t to extract energy from magnetic fields, however, but rotational energy.

You might wonder how this could possibly work, since no information can escape out over the horizon of a black hole. The reason for the speculation is, however, grounded in the so-called Kerr solution to Einstein’s equations, which describes a rotating black hole. For a rotating black hole there is the so-called “stationary limit”, which lies outside the horizon, and a particle travelling with the local speed of light will appear stationary from the outside. More importantly in this case: it is theoretically possible for a particle to have negative energy in this region. Penrose therefore suggested that one could drop a particle from the outside and into this region. In this region the particle should split in two in such a way that one of the particles get negative energy, whereas the other (due to energy conservation) gets more energy. This latter particle would therefore escape back out with more energy than it had when it came in. Voila! Rotational energy extracted from a black hole.

The process nowadays bears the name “The Penrose process”, but has certainly not been physically realised as of yet.

[1] Penrose and Floyd (1971):…/jour…/v229/n6/pdf/physci229177a0.pdf

Ben asks in Benasque

I am sitting in the back of a lecturing room in Centro de Sciencias in Benasque one Thursday in September, starting the blog post from my first scientific conference ever. At the blackboard is a Japanese student speaking about some topic quite inconceivable — partly because of his rather interesting variant of English, and partly due to the technicality with which it is presented. I am tiered. Not that it hasn’t been an interesting conference. To the contrary I have had both an enjoyable stay and intellectual stimulus to the brim. Not only will I return with an enhanced understanding of theoretical cosmology, an extended network of fellow researchers within similar fields to my own and an deepened awareness of the many fields there are under the umbrella of cosmology. Additionally, some of the talks have to some extent shaken me in my faith in science. It is not that I have turned into a disbeliever or anything. I just woke up from my science induced slumber a couple of times, reminded of how easy it is to fall asleep during lectures — even lectures of life. One thing I realized is how insanely many theories there are on the market. Inasmuch as they are non-compatible with each other, they cannot all be right at the same time. I would guess that most theories developed are just quite simply…. wrong. That’s how science goes! You don’t know its wrong before you tried it out. As long as the available evidence is scarce enough, one is free to speculate and invent knew explanations. In theoretical physics we know this. Sometimes one better remember that there is a real world out there, with which your theories have to agree  — or they are quite simply wrong! The fascinating conclusion, however, must still be that physics hits the ground standing on both feet. For even if the individual contribution might seem diminishing in most cases, the combined effort amounts to rather remarkable achievements in terms of falsifiable calculations. Quite frankly we seem to understand more and more physics as the lectures of time goes on. Better just don’t fall asleep, or somebody might whisper you a lie in the ear.

The center was a really good location.
The center was the most fitting place for a conference!

During the talks, the less modernized professors would occasionally express their concerns on the new developments in physics. One day midweek in the midday coffee break one of the defenders of the classical theories blamed the modern cosmologists for picking and choosing according to their own wish, which lead to nothing but sheer speculation and non-sense, he said promptly.
“Well — and that comes from you?” said his colleague, somewhat annoyed, before he added
“But you might as well be right…”
with an ironic, but  disarming smile of phlegmatic diplomacy. I just stood there among the wise grey hairs grinning and hoped for the argument to stretch and last for as long as possible. The lovely atmosphere of rivaling friends would soon be interrupted by an expressive Spanish voice chasing us up for the next session.

One of the nights I ended up dining with an Oxford professor whose opinions on the accelerated expansion of the universe is rather controversial.  Over a five cheese pizza the trust and mistrust, use and abuse of modern science was discussed back and forth. I was rather disturbed (but intrigued) to hear him confirm what rumors had it he pronounced in a lecture at the summer school that was running parallel to our conference at the center. In his preprint uploaded to arXiv, he and two others explain how they “…find, rather surprisingly, that the data are still quite consistent with a constant rate of expansion.“, The data considered in the paper is type 1a supernovae data. I have to say it was a rather interesting dinner. I mean; this is not a nobody; its an Oxford professor!
If there is no accelerated expansion of the universe, the whole community of theoretical physicists are building their theories around evidence that isn’t there. They are all living in a constructed lie that nobody sees.

The venue for the conference was smashing in terms of style and surrounding nature!
The venue for the conference was smashing^^ in terms of style and surrounding nature!

The good thing with science, however, is that the truth seems to pervade in the end, even if it is slowed down by inertia induced by pride, stubbornness or other subjective factors. It pervades due to its explanatory power and simplifying beauty. Anyhow, as I read his paper (actually he is not the first author), I find that his claim is not as strong as I initially thought. Anyhow I am anticipating the discussion to follow if the paper comes out in a high class science journal (and if you were wondering: the big bang theory is not touched by his findings. Rather it would concern the entity typically called dark energy.). The Oxford professor and those who oppose his claims cannot simultaneously be right. One of the parties is wrong. This means one has to be mindful and discerning, even in a discipline like physics, which seemingly is built on pure logic.

The lesson I draw from all this is NOT that theoretical physics is a dead end! But I am reminded that even if the methods we use in physics are rock solid in terms of logic, it doesn’t help if the observational evidence isn’t there to discriminate between the different solutions available from the mathematical side. This is important to remember, and a disclaimer of my own future mistakes 😉 ( which hopefully there will be none of…). Those who believe in science (like myself) must not forget to clearly reveal the assumptions underlying our theories, and those who distrust science must likewise do so on a rational basis, and not cutting it off as wild speculations altogether, without giving a reason for doing so. Remember that — assuming we one day, whether it be gradually or abruptly, will know the truth —  your privileged opinion or personal wishes doesn’t matter for a second in this respect.

I could have gone on to tell you about our hiking to Collo de Toro — a beautiful trip into the surrounding mountains (which reach as high as 3404m on the highest!). Or I could have spelled out the passion of prof. Elizaldes  talk on the origin of the universe, as the Spanish professor gesticulated with his arms and as his voice passionately assumed tones along the whole spectra, all supporting the message he conveyed as he moved back and forth on the floor: much like an actor on stage. His talk pretty much amounted in being a disclaimer of Wikipedia as a good source to information.
Forgetting about the science part of my stay — but not leaving rationalism for a second — I could have rather told you about three lovely conversations I had on the topic of God. At three different occasions, each involving a different person, I had three distinctly characteristic talks on the most profound type of question a human mind can ask: Is there a God? Three bright, young researchers willingly grappled with me on the topic. One of them aggressively. Another reluctant but dismissive and the third one with an open mind.

Yes, I could have told you about this…

…but it would only amount in teaching me another expensive lesson on the constraints provided on the measures of time allotted to each one of us. Instead, therefore, I will stop here.

I hope we shall encounter each other again on a different occasion, though it seems my blogging is not going to increase in frequency. In terms of personal value, I have more profitable things to write (and certainly to do! 🙂 ).

I NEED one of those blackboards in my home if ever I build one... Loved them!
I think I most certainly NEED one of those blackboards in my home if ever I build one… Loved them!

Getting started in Stavanger


Well, it is already soon September, and I am ready to embark upon my Ph.D. work here in the city of dark matter. Indeed it is — I have heard they have a big industry where they mine dark matter from underneath the sea bed here. They call it “oil”. The platforms they use are huge (pic. to the left)! So I am not at all sure why physicists are still asking whether dark matter exists or not… 😉


I have already been working for two weeks by now. There is so much I don’t know, and I have had to read up. Especially on some mathematical tools. Right now I am learning something called the Cartan formalism (Not to be confused with Dashman and the cartoon-formalism!) where something called the orthonormal approach is essential. Though it might not sound like a page turner, it is really quite fun when you finally understand it and see that you can calculate stuff with it. I am finally learning the tools I have wanted to know for quite some time, but never found the time and motivation to read. Today I reproduced the Einstein equations describing space outside a spherically symmetric black hole, and also the equations for a homogeneous, isotropic universe, which has the Big Bang as starting point. Those are text-book examples, but perfect for practice. As soon as I master them I may start applying the tools on new ideas.

I am hoping to be able to blog a bit more seriously about what I am really doing now. Time will show, however, if that really is going to happen, or if it is just another good and empty hope. Surely the life as a Ph. D. student is not a laid back one, so there might be more important stuff that I need to consider doing before blogging. Like drawing cartoons (cf. illustration) or going on conferences. Yes, I am going on a conference already next week!

Sometimes the maths get at me.
Sometimes the maths get at me.

“Cosmology and the Quantum vacuum” is the topic, and it happens to take place in Benasque in Spain. Ah… the struggles of a Ph. D. student… have to get up at 4 am  in the morning to catch the plane to Spain… 😉 My supervisor just let me know that he is going to present our work on viscous cosmology, so I better read up a bit again on what we did. You never know what they will ask. Exciting, though!

Anyways… from the physics side of things it seems that I will work on something related to modified theories of gravity during my studies here in Stavanger. If you have any questions about it, please contact me in a year’s time, and I will let you know what them say… .

At campus: I haven't figured out the meaning of this one yet.
At campus: I haven’t figured out the meaning of this one yet.

After a few years where I have been wondering, pondering and struggling both with questions of faith related character, and with questions concerning what direction my life is to take, I am glad to finally have gotten this opportunity. Actually I am going to work with exactly what I wanted. And I am reunited with my brothers and sister in law, who are also in town. Actually it turns out that the position that I am filling was some sort of a misunderstanding (but I won’t complain about that 🙂 )! The Lord has been good.

I am praying that the time here in Stavanger will do my soul well — seen from the reference frame of eternity.

Significance somewhere insignificant.

Some Sunday in December I find myself in a lecture of life, eagerly taking notes. If my notes during physics lectures have always been sparse, I am trying to make up for it  in the lectures of life. Its funny, isn’t it. In a tiny, cosy little place in a tiny (lovely, perfect, extraordinary etc etc. ) country up north in an insignificant sphere of mass called Tellus in a privileged place in a solar system placing itself in yet another privileged place among a hundred billion stars in an average sized galaxy among a few hundreds of billions of galaxies in our visible universe –and as if it now mattered any more: I front of a chimney — sits  a representative of the human being species  and reflects on the whole universe even to the point of his own existence. No — it’s not funny. It’s is mind-blowing and completely incomprehensible. We are capable of reflection. Of loving, missing, hating and jealousy. We have what we call a conscience. We regret, we feel guilt and we understand moral obligations. Imagination like that found in Victor Hugo’s “Les Miserable”. Brilliance like Schubert’s piano sonatas. Ability as that of the philosopher Kant or the mathematician Euler to comprehend through abstraction. That’s us. Human beings. So privileged among earths creatures. Our eminence is obvious, and yet some say we are but animals. Some say our majesty is crafted by chance and necessity. Others claim there must be a God. Only the blind remains seated on the fence separating the two. No off-fence on his part.




Somehow this — according to some good friends of his; strange — person in front of the chimney experiences a feeling of existence. And much more sophisticated so, he believes, than any animal’s such perception. Just think about it. You recognize yourself in the mirror. That it is “you” (whatever that is…). As obvious as it may sound to have that ability, most animals have yet to demonstrate their capacity to perform such recognition, and it is suggested that even human beings are not born with such an ability. Puzzling, I know. In this ability, I imagine, must be contained an enormous capacity of experiencing life; living as we like to call it. Through it, our perception of reality becomes so much more vivid than that of an animal. Just think of a baby. Do you think a child is capable of as great joys as an adult? By no means. Sure enough; it is able to fill its own measure of joy to the brim. This means that its comparative level of joy — its level of satisfaction —  is possibly more or less complete. No worries, no guilt or bad conscience and a loving mothers nursing bosom to meet all his needs. She provides for her own son, even to the point of dying for him if needed. The only thing the baby does in return is to receive all this unselfish love from the mother’s side and to yearn for more of it. Did you know that a baby’s eyes naturally focus at about a 20-30 cm distance? That should be the distance to a mothers eyes when the baby rests at her breast. No worries, indeed. It occurs rather obvious to me that an adult doesn’t so easily reach this level of satisfaction — even if he is capable of experiencing much more sophisticated joys than that of the baby splashing his spoon in the porridge, or sucking his mothers breast for milk. We therefore clearly see that in our majesty, in our eminent ability to live, there easily develops a backside: With our self-consciousness, follows an increased awareness of right and wrong, and thus a conscience. Hence, inevitably, a bad conscience.  I have the ability to say that I did something wrong, and to feel bad about that. I am a morally obligated being. Some claim there is a way back to the mothers womb. That there is a way back to the peace experienced in caring arms providing for all your needs. These people claim that God sent his own son to die in your place. Others say that’s absurd. ‘Are there still people around believing on those two thousand years old claims?’ they ask. Meanwhile the blind remains seated on the fence.

Finally there remains the mention of the other part of the finite infinity. As the being sits there and enjoys his jolly good cup of tea, he is hardly aware of the staggering 1000 000 000 000 000 cells (10^15) in his body that makes his almost disturbing awareness of existence and enjoyment possible. That is about 10000 times the number of galaxies in the visible universe. There, in that one chair. In that one infinitesimal spot in the already  vast universe. And you know what? Each and ever of those cells on that staggering list are ultra-complex machinery working together in a well-organized, vast universe called ‘the body’. Much like galaxies in the night sky, except they don’t communicate with each other. Communication, you see, is going on all the time in your body. Organizing, developing, regulating and differentiating, all relative to what the other small communities (cells) are doing. Information is being passed in and out of the cells. Signals from the extracellular matrix propagate over the cell membranes and into the cytosol. A signal regulating the expression of a certain gene would further propagate into the nucleus, through mechanisms that are in themselves fancy enough, and finally ensure the altered gene expression.  The genes coded in DNA are themselves too big to get out of the nucleus, and it is anyways better to just bring a copy, as the same recipe will be needed multiple times.  After a thorough and remarkably accurate and quality assessed process of transcription, however,  where the code is rewritten into an RNA-strand, the whole recipe of whatever protein was up for copying (i.e.; if this was one of the  20 000+   protein-encoding genes in the nucleus), is carried away by a messenger (mRNA) into the cytosol. Here ribosomes  attach amino acids after each other according to what the recipe says. Complex mechanisms are involved all along, and we are not yet finished. However, time constraints, the impatience of the reader and a vanishing memory of the author (which should consider having his brain scanned) restrict us to go further into all of it at present. Really; I should blog about this in detail sometime. It is not that I know so much about it, but the little I have learnt, have led me into jaw dropping fascination. If you have never had the opportunity to study this subject, you are in acute danger of thinking that life is easier than it is — in its most biological sense at least… Go borrow a cell biology textbook — it’s a real page turner! All this stuff, all the processes and everything that is going on inside each and every cell. 24 7.  While still coping in med-school I took courage and prompted the professor  in cell biology with the remark that this is so incredible that in fact one might come in danger of making hasty assumptions. You know…I hesitated; one might want to assume there stands a creator behind it all. “Well,” she said, “that it all actually works, is really quite incredible and almost unbelievable. But somehow it does.” Well, then. Question passed in the wrong room. She could just as well have gaped a “I beg you pardon?”.  The actual information in which you are coded is written in a double stranded helix inside each and every cell nucleus in your whole body. This is your DNA, which surely you have heard speaking of. In a haploid cell, there are 3 billion DNA base pairs.  That is YOU spelled out the complete way in every single cell in your body.

The evolutionist will tell you it all started some 3-4 billions of years ago, when cute little cells from the same origin started swimming together in hot pools, multiplying and enjoying the. Much like the aggregated cell lumps called “humans” do to this very day. No matter how superior we are to animals, you see, there is no way you can boast. We are all built on a code remarkably similar to theirs. Wikipedia tells you that 50% of your genes are found in bananas (no wonder some of us go ban..nah… dry joke. Or…sweet, perhaps, but.. ah). We differ no more than 4% from our closest relatives; the chimpanzee. The Bible says that “without God, man is but an animal.”  The student rests his pen and empties his tea. Lecture over. Some fresh air. Some neurons gone crazy up there. Frontal cortex, was it?

The fence is filling up quickly. I hope it will soon break. That people will fall like fruit and like rotten fruit to their respective sides. Gravity is a good thing still.

The gene-ius in us

I just watched a documentary about manipulating genes. In the documentary we among others meet a Chinese girl, Lin Lin, who works as a researcher manipulating pig embryos. Listen to her fluent Chinglish:

 “I still remember the first time I see this embryos under my microscope. And then after 4 months and these embryos they are becoming the pigs. And I am just thinking  oh, these pigs they are used to be the embryos under my microscope, and I make these embryos. I am so exited about that!” -“Why?”, asks the interviewer. “Oh, it is really like being a mum.

This is life that I created. It is by my hand.”

Wow. Those last words belong to nobody but God Almighty. Anyway; so I thought. Manipulating the genome of pigs, the researchers are able to play God, making, molding and shaping individuals according to their own preferences, desires,wishes and ideas about what is best for humankind. The more we know about the genes of individuals, the more precise alterations can be made.  This is not science fiction. Not any more. Combined knowledge of phenotypes (macroscopic traits) and genotypes (an individual’s set of genes) give us rich insight into which genes plays which roles. This is real life, and it is happening daily. What is the goal of it all? At the Beijing Genomics Institute (BGI) in China they have the capacity for sequencing 2000 human genomes per day. Why?

Illustrational; from the documentary.
Illustrational; from the documentary.

To perfect humans, naturally. At least that would be a natural implementation of the information gathered on the institute and its counterparts all around the globe. Just like we perfect tomatoes today, we can increase the power of evolution by going beyond natural selection. Human selection by breeding would be much faster and more controllable.

The sequencing power they have at BGI is enormous, if believing what we hear in the documentary. There seems to be nothing but a matter of time before we for instance understand which genes are responsible for elevated IQ score. It surely will turn out to be a complex affair , but with the combined effort of all the scientist teams around the globe now focusing in on the genetic code and the sequencing of individuals, I can hardly imagine that there is much more than a turtles walk across the road before we are there. As some of the scientists met in the documentary were dreaming about; the population mean IQ score could effectively be increased by picking and choosing our offspring. This would in turn lead to a population willing to change and adapt more efficiently. There would be a much greater human potential to realize. I guess they are right. We would all be smarter. And so it goes with all other desirable traits, too. We will all be more attractive. We will breed extremely caring and self-sacrificing nurses. We will breed heroic and brave soldiers and we will breed strategic leaders. Fantastic, indeed. But really – it is mind blowing to think about. Evolving from one-celled organisms, through some fishy intermediaries crawling up on the shore and all the way through to becoming majestic individuals capable of nothing less than altering their own genomic material! Individuals whose life and future is in their own hands to change and experiment with. Not only your own life. You can soon choose the features of your children. Oh my.

Waiwaiwaiwait. Hold on for just a second. What is actually going on here? A few thousand years back, God looked down at us humans, as in Babel a tower was raised into the heavens. With unrestricted control he said in omnipotence that

” If as one people all sharing a common language they have begun to do this, then nothing they plan to do will be beyond them. Come, let’s go down and confuse their language so they won’t be able to understand each other.” (NET, Gen 11,6-7)

We speak the same language again, and are obviously more connected than anytime before. We research, develop, understand, teach, acquire new skills together with new technology and expand at a higher rate than ever seen before in history. There seem to be no boundaries to what we can do. Soon we will be on Mars. We have thoughts and theories stretching back to the very start of the presently known universe. We can manipulate our own genes or even clone ourselves.

Why does this happen? Where are the boundaries? What does God say when he looks down from heaven today? What about the concepts of spirit and soul that we can read about in the Bible. Where is it? Can we make souls? Many questions that until the present age have seemed artificial and far-fetched are now demanding answers. As Christians I think we will have to face many questions in the future.

What are your thoughts about it?

Flatlanders In 3 Dimensions

It is just as incomprehensible to me that the Flatlanders cannot fathom the depth of a third dimension, as does it strike them as unphysical that there should be one. And then I find myself being a 3 dimensional Flatlander, for it seems so self-evident to me that my mind cannot comprehend 4 spatial dimensions, and I seek no further explanation as to why that is so.

And so it strikes me, that in this world we are all Flatlanders of different dimensionality, but with this one thing in common: If we don’t look up, we will never fathom the depth of reality.

It is hard to see beyond  -- especially if you don't want to.
It is hard to see beyond — especially if you don’t want to.

Oh, did you know that the universe is  about flat? According to the most recent Planc-data the curvature is k= -0.0013 ish. (arXiv: 1303.5076[astro-ph.CO])

A number at last!

I finally have a number. The Friedmann equations together with measurements as a first “guess” seem to permit the expanding universe to have a viscosity as large as about ~ 10^6 Pa s (positive or negative).  1 000 000 Pa s, if you like zeros (and btw; Pa s=kg/(m s)). The shear viscosity of the much denser fluid called “water” (perhaps you encountered it?) is of the order +10^-3, and the bulk viscosity is typically much smaller. The extremely slowly floating fluid called pitch, has a viscosity “only” a hundred times greater (~10^8 Pa s) than that which I here suggest for the universe; the so-called cosmic fluid. This, therefore, is so far a rather peculiar result. So peculiar that it took some time discussing with my supervisor before he quit believed it. You know; I didn’t really have any grasp on how big those numbers ought be, so I just ran over with my results in shear (or perhaps bulk) joy of finally having a number. OK… IT DID strike me as a rather large number, but the universe is extremely large so.. (hehe)…and… I had a number! After months of trying and failing with adding and subtracting letters from the Norwegian and Greek alphabet, the taste of a number is sweet and welcomed — even for a theorist. After all you gotta bow for experiments, and if your theories doesn’t predict anything, there is no way you can test against observations, is there.

Figure 1: Evolution of the Hubble parameter with red-shift when the viscosity parameter is B=0.1. Increasing red-shift corresponds to more and more distant past. Red-shift z=-1 equals infinite future. Red-shift z=0 is at present. The blue and red curves visualize the evolution with positive and negative viscosity, respectively, whereas the black curve gives the viscosity-less solution. Note that the bare eye cannot distinguish the three different scenarios.











The number might just be wrong, though. After all; does the universe exhibit viscous behavior in the first place? Actually there seems to be strong arguments begging explanations if it does not, rather than having to explain why it should. Refer to arXiv:9602128 for a perhaps non-intuitive , yet (in my opinion) quit reasonable, result to this end: Even two ideal expanding fluids should posses viscosity when described as one fluid.

When all comes down to all, fact seems to be that the upper bound so far obtained not necessarily is so far off as a descriptive viscosity (nothing said about it’s cause). As an upper limit, that is. Adding this viscosity to the Friedmann equations almost doesn’t alter the evolution predicted by the standard model (LambdaCDM) at all. Figure 2 shows the evolution when the model is extended with a viscosity term 10 times larger than an upper bound of 10^6 Pa s. Refer to figure 1 and 2 to see that adding negative viscosity seems to fit the data just as well as adding the corresponding positive amount. Negative viscosity corresponds to energy being pumped into the system, and might sound forbidding on thermodynamic grounds, since it seems to violate energy conservation (in 4 dimensional space-time at least). But it seems my supervisor has been speculating in those directions. Refer to arXiv:1306.5634 for interesting details and cosmological models in which the entropy actually decreases with time. If that is correct, the universe will actually acquire a higher and higher degree of order. That should seem weird to most old-ordered fellows. Well; thanks for being so interested in my thesis’ topic that you actually read it all! I know it is interesting… and I am sure you are just as excited as am I to know how adding viscosity to the universe eventually may (or may not) alter it’s final and non-reversible (?) end. It’s fate. It almost feels like it’s fate is in my hands, but I think I might just be exaggerating a bit there… 😉
I find it intriguing, though, that God (who is the one who really decides the fate of his creation!), has made men so small and insignificant, yet capable of making ups his mind about the fate of the whole thing. The whole mega-giga-parsec creation of billions upon billions of galaxies with billions upon billions of stars. We are the center of the universe, aren’t we?

Evolution of the Hubble parameter with red-shift. Increasing red-shift corresponds to more and more distant past. Red-shift z=-1 equals infinite future. Red-shift z=0 is at present.
Figure 2: Evolution of the Hubble parameter with red-shift when the viscosity parameter is B=1. Increasing red-shift corresponds to more and more distant past. Red-shift z=-1 equals infinite future. Red-shift z=0 is at present. The blue and red curves visualize the evolution with positive and negative viscosity, respectively, whereas the black curve gives the viscosity-less solution.

My thesis

Illustration photo, viscous cosmology
Illustration photo

Now that I realized I can link to pdfs on my blog, I figured it will be far easier to post things related to my studies, as I initially intended to. I think there is a way to use Latex in WordPress too, but I haven’t been looking into that yet.  Anyway; this PP-presentation captures the essence of the topic in my thesis. The presentation was given in NFS (Norsk Fysisk Selskap) this spring at the University of Oslo, where I took part in a student conference.

Enjoy: ViscousCosmologyNFS