It would be wonderful if a theory existed that with a minimum of assumptions could explain the initial conditions such as flatness and homogeneity, eliminate all high energy relic particles, and then segue into the big bang model itself by the time of nucleosynthesis. In 1980 Alan Guth proposed such a theory, known as
inflation.1
Inflation
The basic idea of inflation has to do with the rate at which the universe is expanding. When I use the term "rate" in this context I don't mean a speed. In an expanding universe the distances between galaxies are increasing, and the rate of expansion essentially refers to how long it takes for all of those distances to double. (For a more detailed discussion of what the rate of expansion means see my paper "
The Expanding Universe.") In the standard big bang model the universe experiences
power law expansion, meaning the doubling time gets longer as the universe expands. For example, in our current power law expansion distances in the universe were roughly half their current value about 10 billion years ago, but they won't be twice their current value until about 30 billion years from now. By contrast, if the doubling time stays constant then the expansion is referred to as
exponential. Inflationary theory says that before our current power law expansion there was a brief period of exponential expansion.
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Exponential growth can be much faster than power-law growth. In the simplest models of inflation the universe would have expanded by a factor of over ten to the ten million in a fraction of a second. There are two obvious questions raised by this idea: What mechanism would cause such an expansion to occur and what would be the consequences if it did?
In the next section I will discuss the cause of inflation. In the following section I will describe some of the basic consequences of inflation, including the resolution of all the problems raised in the previous section on the big bang model.
Why Inflation Occurs
In general relativity the rate at which the universe expands depends on the average energy density in the universe. If the density is high the expansion is rapid and the doubling time is small. The actual relation is that the doubling time is proportional to one over the square root of the energy density. (This relation is for a flat universe. For an open or closed one it is slightly different. For simplicity I will use the flat universe relation for the rest of this section, but all the basic points would be unchanged if I used the full equation, which is given in a footnote below.) Note that when I talk about energy density I am including the density of matter because relativity says mass is a form of energy. Other forms of energy include, for example, electromagnetic radiation.
In general the expansion rate slows down as the universe expands because the average density decreases. If there are 1000 galaxies in some region of space and all distances double then the volume of space occupied by those galaxies will increase eight times. Since the galaxies have the same total mass as before their density will decrease by eight times. If the mass of galaxies were the only form of energy in the universe then every time distances doubled the doubling time would increase by a factor of the square root of eight. In short a universe whose energy consists entirely of mass will experience power law expansion.
It turns out, however, that other forms of energy behave differently as the universe expands. For example, the energy density contained in light (which is a form of electromagnetic radiation) decreases faster than the energy density of mass. Every time the universe expands by a factor of two the energy density of light decreases not by eight times, but actually by sixteen.
3 So if there is a lot of light energy in the universe the doubling time increases faster than it would for a universe with only mass energy.
One problem that might occur to you with this fact is that the total energy of the universe is apparently not conserved. If a region of space doubled in radius and the energy density in that region did anything other than decrease by a factor of eight then the total energy would change. The resolution of this problem is a somewhat subtle issue in general relativity and involves a kind of gravitational energy, which we cannot directly observe, associated with the expansion of the universe. I'm not going to get into this issue in any detail here. Suffice it to say that while total energy including gravitational potential energy is still conserved, the amount of energy that we can observe in the universe can change as the universe expands. This gravitational energy is not included in the energy density that determines the expansion rate, and from here on when I refer to the energy density of the universe I will be referring to observable energy, whose density can change in a variety of ways as the universe expands.
What kind of energy would we need to have inflation? During inflation the expansion was exponential, or at least nearly so, meaning the doubling time during inflation didn't change much as the universe expanded. This in turn means that the energy density must have been changing very slowly. We know, however, that inflation did not last forever. Thus to explain inflation we would need to find a form of energy that changes very slowly for some period of time, but then begins decreasing rapidly.
We have never observed a kind of energy that acts like this, but according to our current theories of physics there is one. This kind of energy is in the form of a field, so to explain how this works I have to first describe what a field is. The most commonly known example of a field is a magnetic field. A magnetic field has some value everywhere in space. You can test what that value is by placing a magnet, e.g. a compass, in that spot and seeing how it reacts. Even in the absence of any objects for it to act on, though, a magnetic field by itself has a certain amount of energy. In addition to magnetic fields there are other types such as electric fields, gravitational fields, and so on. In general any field is defined by having some measurable value at every point in space and having an energy density that depends on that value.
Different kinds of fields react differently to the expansion of the universe. For example, I noted above that the energy density of electromagnetic radiation decreases faster than that of ordinary matter. It turns out that there is one particular kind of field with the property that when its energy density is very large that density decreases very slowly as the universe expands. When its energy density decreases past a certain point it stops behaving this way and starts decreasing at the same rate as ordinary matter. Such a field is called a
scalar field. I'm not going to explain here what one is or why it behaves in this way; this is just one of those things that you will have to take my word about.
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Inflation doesn't require precise exponential expansion. Rather there is a set of mathematical criteria for how close to exponential the expansion needs to be during inflation, i.e. how much the doubling time can change each time distances double, in order for inflation to still have the consequences described below. Given a scalar field with a high enough energy density these conditions will be met and the expansion of the universe can be considered
quasi-exponential. In general, however, the energy density of a scalar field is not perfectly constant as the universe expands. Rather it decreases more rapidly the smaller it is, such that eventually when it becomes small enough the universe enters a stage of power-law expansion.
So in order for inflation to have occurred it suffices that some scalar field exists and at some point in the past it had a very large energy density. It's true that we have never to date observed a scalar field, but physicists believe for a variety of theoretical reasons that many of them probably do exist and that we will start to see them in our next generation of particle accelerators. The second requirement, however, requires some thought. Having a scalar field with a large energy density is in many ways like having a very strong magnetic field. If I told you that the early universe was filled with strong magnetic fields you would be justified in wondering why that was so. Recall that the "initial conditions" for our universe were set by physics that we don't know occurring above the Planck scale. So it might be that somewhere in the universe a region emerged with a large value of a scalar field, but why would this have happened simultaneously throughout the whole universe?
The answer is that it wouldn't need to. Suppose that when the universe first started to have sub-Planckian density it was filled with many different regions in which all the fields had very different values. All we require for inflation is that somewhere there was one region, no matter how small, where the largest contribution to the energy came from a high-energy scalar field. If that happened then that small region would inflate, almost instantly growing much larger than all the other regions around it. Very soon this inflationary region would occupy nearly 100% of the total volume.
This point is possibly the most important one in the paper. For that reason it bears repeating, and I urge you to think about it carefully. In the standard big bang model the entire universe started expanding uniformly at the same moment. In the inflationary scenario I am describing this expansion began with an exponential growth in only one small part of the universe while the rest of it either grew in a power law or started shrinking. However this one inflationary region became so big that everything we can see, or will probably ever be able to see, lies within it. Thus the universe appears to us to be uniform, even though on much larger scales it is not.
XI Wiki
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Originally Posted by Pirian
Considering we know next to nothing beyond plank scales, that kind of paper is nothing but mathematical masturbation (nothing wrong with it, that's how you find new theories). You postulate something (a field, the interior of a black hole, x amount of energy accumulated in y space), solve Einstein field equation and see if it can evolve into an universe that share similar caracteristic to our.
