inflationary multiverse – fractalizing time

Standard Big Bang theory says that everything begins with a big bang, a huge explosion. Terrorists started the universe. But when you calculate how much high tech explosives these guys would have to have at their disposal to start the universe formation, they would need 1080 tons of high tech explosives, compressed to a ball smaller than 1 centimeter, and ignite all of its parts exactly at the same time with precision better than 1 in 10,000.

According to inflationary theory, one may avoid many of these problems if the universe began in some special state, almost like a vacuum-like state. The simplest version of such a state involves something called “scalar field.” Remember electric and magnetic fields? Well, scalar field is even simpler, it does not point to any direction. If it is uniform and does not change in time, it is invisible like vacuum, but it may have lots of energy packed in it. When the universe expands, scalar field remains almost constant, and its energy density remains almost constant.

Think about the universe as a big box containing many atoms. When the universe expands two times, its volume grows eight times, and therefore the density of atoms decreases eight times. However, when the universe is filled with a constant scalar field, its energy density remains constant when the universe expands. Therefore when the size of the universe grows two times, the total energy of matter in the universe grows eight times. If the universe continues to grow, its total energy (and its total mass) rapidly becomes enormously large, so one could easily get all of these 1080 tons of mater starting from almost nothing. That was the basic idea of inflation.

Not everyone knows that when the universe expands, the total energy of matter does change. The total energy of matter plus gravity does not change, and it amounts to exactly zero. So the energy conservation for the universe is always satisfied, but it is trivial: zero equals zero. But we are not interested in the energy of the universe as a whole; we are interested in the energy of matter.

If we can have a regime where we have some kind of instability where the initial zero energy can split into a very big positive energy of matter, and a very big negative energy of gravity, the total sum remains zero. But the total energy of matter can become as large as we want. This is one of the main ideas of inflation.

We have found how to start this instability, and how to stop it, because if it doesn’t stop, then it goes forever, and then it’s not the universe where we can we live. … My idea was how to start it, continue it, and eventually stop it without damaging the universe. …

… I could start in a red part of the universe, like in the Soviet Union, and you can start in a blue universe, and then, after inflation, after each part becomes exponentially large, each of us would look around and say, just like Einstein and Newton did: “This is the universe, this is the whole thing, it is single-colored.” And then some of us will try to explain why the universe must be red, and others will try to explain why the universe must be blue, all over the world. But now we know that from the point of view of inflation, it’s quite possible that our universe is divided into many regions with different properties. Instead of the cosmological principle that asserted that the whole world is the same everywhere and all of us must live in the parts of the universe with similar properties, we are coming to a more cosmopolitan perspective: We live in a huge inflationary multiverse. Some of us can live in its red parts, some can live in blue parts, and there is nothing wrong about this picture as long as each of its parts is enormously large because of inflation.

I found that in the first model of new inflation, which I invented back in 1981, the universe could expand 10800 times during the inflationary stage. It was surreal; we have never seen numbers like that in physics. When I was giving my first talks on new inflation at Lebedev Physical Institute, where I invented this theory, I had to apologize all the time, saying that 10800 was way too much. Probably later, I said, we’ll come to something more realistic, the numbers will decrease and everything will become smaller. But then I invented a better inflationary theory, the theory of chaotic inflation, and the number became 101000000000000. And then I found that inflation in this theory may continue eternally.

… [follow the link below to Andrei Linde’s talk because it is really an example of how the best theory and the best physics even if it involves the whole universe has a humorous quality and lots of funny stories] …

Interestingly, most of the books on astronomy still describe inflation as exponential expansion during the cosmological phase transitions; this theory was so popular that nobody even noticed that it died back in `82. But a year later, in ’83, I invented a different scenario, which was actually much simpler. It was chaotic inflation, and it did not require the universe to be hot to start with.

… I abandoned the idea of the cosmological phase transitions, metastability, false vacua …

In chaotic inflation, where the potential energy has the simplest parabolic form, no specifically flat pieces of potential are required, you just take a model like that, and if the field is sufficiently high, there are quantum fluctuations, and the scalar field wants to go down, but quantum fluctuations sometimes throw it higher. The probability of jumping high is very small, but if you jump, you are exponentially rewarded by the creation of huge amounts of new volume of the universe. You start with a tiny part of the universe, and then it just spreads and spreads. It’s like a chain reaction. It is called “branching diffusion process.”

In the paper of ’86 where I discovered eternal chaotic inflation, I also noted that if you have eternal inflation in string theory, then the universe will be divided into enormous number of different exponentially large parts with different properties corresponding to large number of different stringy vacua, and that’s an advantage. That was what later became string theory landscape.

… quantum fluctuations become essentially classical when the universe becomes large. They give rise to galaxy formation.

If you marry string theory with the theory of eternal inflation, then one can have one type of vacuum in one part of the universe, another vacuum in another part of the universe, and it is possible to jump from one vacuum to another due to quantum effects. Lenny Susskind gave this scenario a very catchy name, string theory landscape.

… when we’re talking about this vacuum state, vacuum state means homogenous state describing our three dimensions, three dimensions plus one. But the remaining six dimensions, they may squeeze like this, or they may squeeze like that. There are lots of different topologies in it. In addition to different topologies, there are different fields, which may exist in this six-dimensional space, so-called fluxes.

… in ’86 we did not know a single example of a stable string theory vacuum; we just expected that there should be exponentially many such vacua. In 2003 we learned how to find such vacua, and then it was realized that indeed there a lots and lots of them. So that is the present view.

… 10500 is an abnormally large number, it tells you how many choices of vacua do you have. You have this huge amount of possibilities. And by the way, there is a question, which many people ask: “How do you know?” How do we know that we have this multitude, that these other parts of the universe are somewhere inside our universe?

This is the picture: the universe is very, very big, and it is divided into parts. Here is one realization of the string of vacua. There, in the same universe, but far away from us, it’s a different vacuum. The guys here and there do not know about each other because they’re exponentially far apart. That’s important to understand in order to have a vision of the universe. It’s important that you have a choice. But if you do not see these parts, how do you know that they actually exist, and why do you care?

Usually I answer in the following way: If we do not have this picture, then we cannot explain many strange coincidences, which occur around us. Like why vacuum energy is so immensely small, incredibly small. Well, that is because we have many different vacua, and in those vacua where vacuum energy is too large, galaxies cannot form. In those vacua, where energy density is negative, the universe rapidly collapses, and in our vacuum the energy density is just right, and that is why we live here. That’s the anthropic principle. But you cannot use anthropic principle if you do not have many possibilities to choose from. That’s why multiverse is so desirable, and that’s what I consider experimental evidence in favor of multiverse.

How many possibilities are there? And the answer, and this is purely a combinatorial answer, is that if n is the number of times the size of the universe doubled during inflation, and you take 23n, this will show you the volume of the universe after inflation. Where the volume grows by 23n, the total number of possible configurations, which may occur there because of these quantum jumps, will be also proportional to 23n. This will give you the total number of possible configurations of matter that you can produce during inflation, and this number typically is much, much greater than 10500.

… inflation goes forever, so one could even expect that this number is infinite. However, during eternal inflation each jump can be repeated; it can repeat itself. Scalar field jumps again to the state where it jumps again, to a state where it jumps again, and eventually it start producing identical configurations of matter.

Think about it this way: previously we thought that our universe was like a spherical balloon. In the new picture, it’s like a balloon producing balloons, producing balloons. This is a big fractal. The Greeks were thinking about our universe as an ideal sphere, because this was the best image they had at their disposal. The 20th century idea is a fractal, the beauty of a fractal. Now, you have these fractals. We ask, how many different types of these elements of fractals are there, which are irreducible to each other? And the number will be exponentially large, and in the simplest models it is about 10 to the degree 10, to the degree 10, to the degree 7. It actually may be much more than that, even though nobody can see all of these universes at once.

– Andrei Linde from here