A few weeks ago I was talking about the concept of Brane Multiverse which gains attention of physicists concerned with the superstring theory (or, equivalently, with the M-theory). Then, I showed how the Cyclic Multiverse model was improved upon the notions of this theory. Today our goal is to have a look on another Multiverse model that was also developed by the string theorists. The following concept may, in some moments, be a little bit vague and confusing since it isn’t easy to visualize and not at all easy for me to explain. So I encourage all the interested readers, who will struggle to conceptually grasp some of the following aspects, to read Brian Greene’s book “The Hidden Reality” which is the main reason behind this series of articles.

As you might remember from the previous articles, the string theory’s ultimate purpose is a unification of the laws of physics and, particularly, finding an approach that would be consistent with both general relativity and quantum mechanics. String theory claims that all the elementary particles hide tiny vibrating filaments of energy within themselves and, also, that our Universe has 11 dimensions, not 4. For the purposes of this article I shall need to introduce a couple of even more subtle concepts such as fluxes, quantum tunneling and anthropic principle. But first, we need to recall something about the cosmological constant.

You might think that the difference between 0 and 0.000000000000000000000000000000000000000000000000000000000

0000000000000000000000000000000000000000000000000000000000000001 is completely negligible. This is certainly true for any normal measurements, but as it turns out, sometimes such an infinitesimal difference could play a significant role in the way entire Universe behaves and it could even be responsible for my opportunity to write this article and for yours to read it. Yes, you’ve got it right, this tiny magnitude represents the value of what is known as the cosmological constant which could be responsible (among other things) for the possibility of our form of life to take hold.

I’m not going to describe here how the results leading to the non-zero cosmological constant were obtained, but if you are not familiar with it – here is another article taking this question into consideration, and here is another one on the related topic written by the member of our society, Mohnish Pandey. What’s interesting for us here is the question as to why the value of this mysterious Dark Energy is equal to this peculiar number given above (which is, scientifically speaking, 10 to the power of negative 123) and not just zero. If we look at the process of inflation, which is thought to have taken place a tiny fraction of a second after the Big Bang, we see that the inflaton field tends to occupy the lowest energy state that have long been thought to be zero. In the image below you can see that the energy density is on its very high level in the moment of inflation, and then it drops down to its lower energy state which, as we just saw, was thought to be equal to zero. (You can imagine a ball rolling down from the summit of a mountain to the bottom-land. We shall need this analogy later in this article.)

However, when Saul Perlmutter and Brian Schmidt published the results of their teams, physicists have been of necessity to assume that the actual value of cosmological constant does not equal zero. This is where the anthropic principle comes into play.

We’ve long known that neither mankind nor Earth are the center of the Universe. This so-called Copernican principle has been proven for countless times and is now the basis of modern-day cosmology. We know that our planet is not at the center of the Solar system, the Solar system is not at the center of the Milky Way, and there is no center of the Universe at all, hence the Milky Way can’t be at the center of the Universe either. But despite the fact that there is no doubt about all these statements, we must concede that our position certainly plays a significant role in our own observations. That is, the fact that we are able to make our observations and to do various experiments tells us that certain fundamental features of our Universe, such as the mass of an electron, the existence of the Higgs field and the like, yield certain conditions hospitable for our existence, otherwise we just would not be here. This idea, originally proposed by an Australian physicist Brandon Carter, is called the anthropic principle and it has two separate branches: weak anthropic principle and strong anthropic principle, which we need not be concerned with for the purpose of this article.

One of the great physicists who have taken this principle seriously was Steven Weinberg. In 1980s Weinberg appears to have stated that, according to his calculations, if the value of cosmological constant were way higher than observed – its repulsive force would prevent the formation of galaxies, and if this value were much lower – such a Universe would collapse on itself before any galaxy could form. And with no galaxies there are no stars, no planets and no possibility for life to exist in such a Universe. Weinberg has also calculated that for our Universe, with its particular value of cosmological constant, to naturally emerge among the vast complex of different Universes with various values of cosmological constant, their amount has to vastly exceed the number of elementary particles in the observable Universe.

If this is actually true, our question as to why the measured value of the cosmological constant has its peculiar magnitude would be completely misguided. It is similar to the famous story of Johannes Kepler looking for an answer to the question as to why the Earth is located exactly 93 million miles from the Sun. He spent many years trying to find the answer in terms of physical laws but he never succeeded. This is definitely because the physics doesn’t have an answer to this question at all. In the last 20 years we’ve discovered thousands of exoplanets largely varying in distance from their home stars, therefore trying to find a particular distance from a planet to its host star is just completely wrong-headed. Of course, we can’t blame Kepler for that since he couldn’t know about planets outside of our Solar system. But I mentioned this story because in the case of vast amount of Universes, each with its own distinctive magnitude of the cosmological constant, our attempts of finding the answer to our question in terms of physics would also be wrong-headed. Now you might ask whether there is a mechanism that would be capable of explaining how the number of Universes might be so overwhelmingly huge. As it turns out, we know of such a mechanism which involves both inflationary cosmology and the string theory.

As you might remember, the fundamental features of the Universe are highly dependent upon the shapes of extra-dimensions according to the string theory. Initially there were just several possible shapes but as new methods of research were developed, the number of these shapes increased up to hundreds and even thousands. This is a huge, but still, manageable collection. However, when the string theorists understood that strings are not the only entity of the theory, but there are also branes, it became clear that for a precise description of each shape we have to take into account what is known in physics as the flux. You can imagine an electron that creates electric field around itself or a magnet that creates magnetic field. Similarly, a brane creates such a field around itself which we now call a brane field. I don’t want to go too much into details here but what is of particular relevance for us is that the necessity of taking these fluxes into account increased the amount of possible shapes of extra-dimensions to unimaginable 10 to the 500^{th} power! And if we combine the concept of eternal inflation with the string theory we can obtain this number of Universes, each with its own shape of extra-dimensions.

To get the entire picture of our landscape we now need to improve our notion of mountains and bottom-lands. For this purpose we have to obtain some familiarity with the very obscure notion of quantum mechanics which is called quantum tunneling. Imagine yourself driving a car with a high speed. One moment, as a result of very unfortunate circumstances, you’ve come to a situation when your car is inevitably going to crash into another. Since this situation is inevitable, nothing you could do to prevent it in our human world. But if you somehow managed to enter the world of quantum mechanics, at the moment of crash you could have tunneled through another car and be in safety. This is an aspect of yet another thing which we would not even exist without. Quantum tunneling allows the stars to shine and their light gives us warmth that makes our environment hospitable. Let me explain this a little bit deeper. The energy which stars give off is a result of nuclear fusion inside their cores. Hydrogen is being fused into helium, the process where 4 hydrogen atomic nuclei, each consisting of 1 proton, are being transformed into 1 helium atomic nucleus consisting of 2 protons and 2 neutrons. The initial state with 4 hydrogen nuclei possesses higher amount of energy than the second. But according to the conservation of energy, this excess should be given off in this process. This is exactly the light you see. But for 2 protons to smack together they need to overcome the repulsive force of their electric charges (each proton has electric charge of positive 1). And the amount of energy these protons possess is not enough for this to happen, and from the classical point of view the nuclear fusion could not have occurred to produce any sufficient amount of energy for life to exist on the planets orbiting a star. But on the quantum level particles have a tiny probability to suddenly appear in a ‘slightly different place’. In our cars analogy you would have such a tiny probability to tunnel through the other car. This is essentially just a matter of probability, but the amount of elementary particles inside the core of our Sun for example is so huge that quantum tunneling occurs perpetually. This is what makes nuclear fusion possible.

Now we have to remember that after inflaton rolled down to the bottom-land it has given off all of its energy, but our Universe still has quantum fluctuations of various fields occurring everywhere through the space, and we also have the Higgs field possessing some energy. So we now have to update our picture with other mountains and bottom-lands each of those would vary in the energy density.

The picture above represents our landscape where you can see mountains and bottom-lands. The height of each particular part of this landscape corresponds to the energy density. Mountains correspond to the high energy levels where inflation occurs, whereas bottom-lands correspond to the lower energy states where inflation has stopped and a bubble-Universe emerged. Accordingly, the lower a bottom-land is placed on the map the lesser energy corresponding Universe possesses. Now, what about quantum tunneling and this landscape you might ask. The trick here is that the entire Universe, placed in some bottom-land on our map, might quantum tunnel through the closest peak and to find itself in another bottom-land with a lower energy state than the previous one.

It might also tunnel to the higher energy state, but according to the math this is extremely unlikely. So if this idea sounds compelling for you, our Universe has found itself in the bottom-land with this particular cosmological constant value which is equal to 10 to the power of negative 123.

This is the Landscape Multiverse.

Next time I shall be talking about the Quantum Multiverse which some of you may be familiar with as Many-Worlds Interpretation.

I thank everybody for your time and see you next time.

Happy New Year everyone!

Great Job Aleksei! This is very well written. Thank you for continuing to bring new ideas and helping me to understand more and more about our Universe!

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My pleasure! Thank you for the feedback!

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Thanks Aleksei, that was fascinating and well written! It opens up a whole area of discussion about the nature of our Uninverse and the possibilty put forward by some researchers, that our Universe might one day suddnely drop to a lower energy level, which would be bad news for yanyone living in it. Fortunately this would happen at the speed of light so we wouldn’t know about it.

Happy New Year to oyu too!

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thanks a lot for such a great feedback, Peter!

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