The Inflationary Universe

May 1, 2003 by Alan Harvey Guth

What happened before the Big Bang and why is the universe uniform and flat? The inflationary model offers an explanation. It also predicts the observed non-uniformities of the cosmic background radiation based on wild ideas about quantum fluctuations at 10^-35 seconds. Next step: the intersection between cosmology and particle physics.

Originally published on Edge, Nov. 7, 2002. Published on April 30, 2003.

On July 21, 2002, Edge brought together leading thinkers to speak about their "universe." Other participants:

The Computational Universe by Seth Lloyd
The Emotion Universe by Marvin Minsky
The Intelligent Universe by Ray Kurzweil
The Cyclic Universe by Paul Steinhardt

Paul Steinhardt did a very good job of presenting the case for the cyclic universe. I’m going to describe the conventional consensus model upon which he was trying to say that the cyclic model is an improvement. I agree with what Paul said at the end of his talk about comparing these two models; it is yet to be seen which one works. But there are two grounds for comparing them. One is that in both cases the theory needs to be better developed. This is more true for the cyclic model, where one has the issue of what happens when branes collide. The cyclic theory could die when that problem finally gets solved definitively. Secondly, there is, of course, the observational comparison of the gravitational wave predictions of the two models.

A brane is short for membrane, a term that comes out of string theories. String theories began purely as theories of strings, but when people began to study their dynamics more carefully, they discovered that for consistency it was not possible to have a theory which only discussed strings. Whereas a string is a one-dimensional object, the theory also had to include the possibility of membranes of various dimensions to make it consistent, which led to the notion of branes in general. The theory that Paul described in particular involves a four-dimensional space plus one time dimension, which he called the bulk. That four-dimensional space was sandwiched between two branes.

That’s not what I’m going to talk about. I want to talk about the conventional inflationary picture, and in particular the great boost that this picture has attained over the past few years by the somewhat shocking revelation of a new form of energy that exists in the universe. This energy, for lack of a better name, is typically called "dark energy."

But let me start the story further back. Inflationary theory itself is a twist on the conventional Big Bang theory. The shortcoming that inflation is intended to overcome is the basic fact that, although the Big Bang theory is called the Big Bang, it is in fact not really a theory of a bang at all; it never was. The conventional Big Bang theory, without inflation, was really only a theory of the aftermath of the Bang. It started with all of the matter in the universe already in place, already undergoing rapid expansion, already incredibly hot. There was no explanation of how it got that way.

Inflation is an attempt to answer that question, to say what "banged," and what drove the universe into this period of enormous expansion. Inflation does that very wonderfully. It explains not only what caused the universe to expand, but also the origin of essentially all the matter in the universe at the same time. I qualify that with the word "essentially" because in a typical version of the theory, inflation needs about a gram’s worth of matter to start. So, inflation is not quite a theory of the ultimate beginning, but it is a theory of evolution that explains essentially everything that we see around us, starting from almost nothing.

The basic idea behind inflation is that a repulsive form of gravity caused the universe to expand. General relativity from its inception predicted the possibility of repulsive gravity; in the context of general relativity you basically need a material with a negative pressure to create repulsive gravity. According to general relativity it’s not just matter densities or energy densities that create gravitational fields; it’s also pressures. A positive pressure creates a normal attractive gravitational field of the kind that we’re accustomed to, but a negative pressure would create a repulsive kind of gravity.

It also turns out that according to modern particle theories, materials with a negative pressure are easy to construct out of fields which exist according to these theories. By putting together these two ideas—the fact that particle physics gives us states with negative pressures, and that general relativity tells us that those states cause a gravitational repulsion—we reach the origin of the inflationary theory.

By answering the question of what drove the universe into expansion, the inflationary theory can also answer some questions about that expansion that would otherwise be very mysterious. There are two very important properties of our observed universe that were never really explained by the Big Bang theory; they were just part of one’s assumptions about the initial conditions. One of them is the uniformity of the universe—the fact that it looks the same everywhere, no matter which way you look, as long as you average over large enough volumes. It’s both isotropic, meaning the same in all directions, and homogeneous, meaning the same in all places.

The conventional Big Bang theory never really had an explanation for that; it just had to be assumed from the start. The problem is that, although we know that any set of objects will approach a uniform temperature if they are allowed to sit for a long time, the early universe evolved so quickly that there was not enough time for this to happen. To explain, for example, how the universe could have smoothed itself out to achieve the uniformity of temperature that we observe today in the cosmic background radiation, one finds that in the context of the standard Big Bang theory, it would be necessary for energy and information to be transmitted across the universe at about a hundred times the speed of light.

In the inflationary theory, this problem goes away completely, because in contrast to the conventional theory it postulates a period of accelerated expansion while this repulsive gravity is taking place. That means that if we follow our universe backwards in time towards the beginning using inflationary theory, we see that it started from something much smaller than you ever could have imagined in the context of conventional cosmology without inflation. While the region that would evolve to become our universe was incredibly small, there was plenty of time for it to reach a uniform temperature, just like a cup of coffee sitting on the table cools down to room temperature. Once this uniformity is established on this tiny scale by normal thermal-equilibrium processes—and I’m talking now about something that’s about a billion times smaller than the size of a single proton—inflation can take over, and cause this tiny region to expand rapidly, and to become large enough to encompass the entire visible universe. The inflationary theory not only allows the possibility for the universe to be uniform, but also tells us why it’s uniform: It’s uniform because it came from something that had time to become uniform, and was then stretched by the process of inflation.

The second peculiar feature of our universe that inflation does a wonderful job of explaining, and for which there never was a prior explanation, is the flatness of the universe—the fact that the geometry of the universe is so close to Euclidean. In the context of relativity, Euclidean geometry is not the norm; it’s an oddity. With general relativity, curved space is the generic case. In the case of the universe as a whole, once we assume that the universe is homogeneous and isotropic, then this issue of flatness becomes directly related to the relationship between the mass density and the expansion rate of the universe. A large mass density would cause space to curve into a closed universe in the shape of a ball; if the mass density dominated, the universe would be a closed space with a finite volume and no edge. If a spaceship traveled in what it thought was a straight line for a long enough distance, it would end up back where it started from.

In the alternative case, if the expansion dominated, the universe would be geometrically open. Geometrically open spaces have the opposite geometric properties from closed spaces. They’re infinite. In a closed space two lines which are parallel will start to converge; in an open space two lines which are parallel will start to diverge. In either case, what you see is very different from Euclidean geometry. However, if the mass density is right at the borderline of these two cases, then the geometry is Euclidean, just like we all learned about in high school.

There are two primary predictions that come out of inflationary models that appear to be testable today. They have to do (1) with the mass density of the universe, and (2) with the properties of the density non-uniformities. I’d like to say a few words about each of them, one at a time. Let me begin with the question of flatness.

[Continued on Edge]

Copyright © 2002 by Edge Foundation, Inc. Published on with permission.