### Evidence for Inflation

So far I have tried to describe how inflation works, but now I would like to explain the reasons why many scientists - including certainly myself - believe that inflation really is the way that our observed universe began. There are six reasons that I will discuss, starting with some very general ideas and then moving to more specific ones.

The first reason is the obvious statement that the universe contains a tremendous amount of mass. It contains about 1090 particles within the visible region of the universe. I believe that most non-scientists are somewhat puzzled to hear anyone make a fuss over this fact, since they think, Of course the universe is big - it's the whole universe! However, to a theoretical cosmologist who is hoping to build a theory to explain the origin of the universe, this number seems like it could be an important clue. Any successful theory of the origin of the universe must somehow lead to the result that it contains at least 1090 particles. The fundamental theory on which the calculation is based, however, presumably does not contain any numbers nearly so large. Calculations can of course lead to factors of 2 or π, but it would take very many factors of 2 or π to reach 1090. Inflation, however, leads to exponential expansion, and that seems to be the easiest way to start with only small numbers and finish with a very large one. With inflation the problem of explaining why there are 1090 or more particles is reduced to explaining why there were 100 or more doubling times of inflation. The number 100 is modest enough so that it can presumably arise from parameters of the underlying particle physics and/or geometric factors, so inflation seems like just the right kind of theory to explain a very large universe.

The second reason is the Hubble expansion itself - the fact that the universe is observed to be in a state of uniform expansion. An ordinary explosion, like TNT or an atomic bomb, does not lead to expansion that is nearly uniform enough to match the expansion pattern of the universe. But the gravitational repulsion of inflationary models produces exactly the uniform expansion that was first observed by Edwin Hubble in the 1920s and 30s.

Third, inflation is the only theory that we know of that can explain the homogeneity and isotropy of the universe - that is, the uniformity of the universe. This uniformity is observed most clearly by looking at the cosmic microwave background radiation, which we view as the afterglow of the heat of the big bang. The intensity of this radiation is described by an effective temperature, and it is observed to have the same temperature in every direction to an accuracy of about one part in a hundred thousand, after we correct for our own motion through the cosmic background radiation. In other words, this radiation is incredibly smooth. As an analogy we can imagine a marble that has been ground so smoothly that its radius is uniform to one part in a hundred thousand. The marble would then be round to an accuracy of about a quarter of the wavelength of visible light, about as precise as the best optical lenses that can be manufactured with present-day technology.

In the standard big bang theory there is no explanation whatever for this uniformity. In fact, one can even show that within the context of the standard big bang theory, no explanation for this uniformity is possible. To see this, we need to understand a little about how this cosmic background radiation originated. During the first approximately 300,000 years of the history of the universe, the universe was hot enough so that the matter was in the form of a plasma - that is, the electrons were separated from the atoms. Such a plasma is very opaque to photons, which are constantly scattered by their interactions with the free electrons. Although the photons move of course at the speed of light, they change directions so rapidly that they essentially go nowhere. During the first 300,000 years of the history of the universe, the photons were essentially pinned to the matter.

But after 300,000 years, according to calculations, the universe cooled enough so that the plasma neutralized. The free electrons combined with the atomic nuclei to form a neutral gas of hydrogen and some helium, which is very, very transparent to photons. From then on these photons have traveled in straight lines. So, just as I see an image of you when I observe the photons coming from your face, when we look at the cosmic background radiation today we are seeing an image of the universe at 300,000 years after the big bang. Thus, the uniformity of this radiation implies that the temperature must have been uniform throughout this whole region by 300,000 years after the big bang.

To think about whether the temperature of the observed universe could have equilibrated by this early time, we could try to imagine fancifully that the universe was populated by little purple creatures, whose sole purpose in life was to make the temperature as uniform as possible. We could imagine that each purple creature was equipped with a little furnace, a little refrigerator, and a cell phone so that they could communicate with each other. The communication, however, turns out to be an insurmountable problem. A simple calculation shows that in order for them to achieve a uniform temperature by 300,000 years, they would need to be able to communicate at about a hundred times the speed of light. But nothing known to physics allows communication faster than light, so even with dedicated purple creatures we could not explain the uniformity of the cosmic background radiation.

So in the standard version of the big bang theory, before inflation is introduced, one simply has to hypothesize that the universe started out uniform. The initial uniformity would then be preserved, since the laws of physics are by assumption the same everywhere. This approach allows one to accommodate the uniformity of the universe, but it is not an explanation.

Inflation gets around this problem in a very simple way. In inflationary theories the universe evolves from a very tiny initial patch. While this patch was very small, there was plenty of time for it to become uniform by the same mechanism by which a slice of pizza sitting on the table cools to room temperature: things tend to come to a uniform temperature. Once this uniformity is established on the scale of the very tiny patch, inflation can take over and magnify the patch to become large enough to encompass everything that we observe. Thus, inflation provides a very natural explanation for the uniformity of the universe.

Reason number four is known as the flatness problem. It is concerned with the closeness of the mass density of our universe to what cosmologists call the critical density. The critical density is best defined as that density which would cause the universe to be spatially flat. To understand what this means, one must understand that, according to general relativity, the geometry of space is determined by the matter that it contains. If the mass density of the universe is very high, the space will curve back on itself to form a closed universe, the three-dimensional analogue of the two-dimensional surface of a sphere. The sum of the angles in a triangle would exceed 180o, and parallel lines would meet if they are extended. If the mass density is very low, the space would curve in the opposite way, forming an open universe. The sum of the angles in a triangle would then be less than 180o, and parallel lines would diverge if they were extended. But with just the right mass density (for a given expansion rate) the spatial geometry will be exactly Euclidean, just like what we all learned in high school - 180o in every triangle, and parallel lines remain parallel no matter how far they are extended. This borderline case is the critical density.

Cosmologists use the Greek letter Ω (Omega) to denote the ratio of the average mass density of the universe to the critical density:

Today there is growing evidence that Ω is equal to one to within about 10%,but the issue is not completely settled. For purposes of this discussion, therefore, I will begin with the uncontroversial statement that Ω lies somewhere in the interval between 0.1 and 2.

You would probably not expect that much could be concluded from such an noncommittal starting point, but in fact it tells us a lot. When one looks at the equations describing the evolution of the universe, it turns out that Ω = 1 is an unstable equilibrium point, like a pencil balanced on its tip. If the pencil is started exactly vertical and stationary, the laws of Newtonian mechanics imply that it will remain vertical forever. But if it is not absolutely vertical, it will rapidly start to fall in whichever direction it is leaning. Similarly, if Ω began exactly equal to 1, it would remain 1 forever. But any deviation from 1 will grow rapidly as the universe evolves. Thus, for Ω to be anywhere in the ballpark of 1 today, it must have started extraordinarily close to 1. For example, if we extrapolate backwards to 1 second after the big bang, Ω must have been 1 to an accuracy of 15 decimal places. While 1 second may sound like an extraordinarily early time at which to be discussing an 11- to 16-billion-year-old universe, cosmologists have pretty much confidence in the extrapolation. The nucleosynthesis processes, which are successfully tested by present measurements of the abundances of the light chemical elements, where already beginning at 1 second after the big bang.

In fact, particle theorists like myself are attempting to push the history of the universe back to what we call the Planck time, about 10-43 seconds, which is the era when quantum gravity effects are believed to have been important. Since our understanding of quantum gravity is still very primitive, we generally make no attempt to discuss the history of the universe at earlier times. But if we attempt to extrapolate the history of the universe back to the Planck time without invoking inflation, we find that Ω at the Planck time must have been equal to 1 to an accuracy of 58 decimal places.

Without inflation, there is no explanation for the initial value of Ω. The big bang theory is equally self-consistent for any initial value of Ω, so one has no a priori reason to prefer one value over another. But if the theory is to agree with observation, one must posit an initial value of Ω that is extraordinarily close to 1.

With inflation, on the other hand, during the brief inflationary era the evolution of Ω behaves completely differently. Instead of being driven away from 1, during inflation Ω is driven very strongly towards 1. So with inflation you could assume that Ω started out as 1, 2, 10, 103, or 10-6. It doesn't matter. As long as there was enough inflation, then Ω would have been driven to 1 to the extraordinary accuracy that is needed.

The fifth reason for believing the inflationary description is the absence of magnetic monopoles. Grand unified particle theories, which unify all the known particle interactions with the exception of gravity, predict that there should be stable particles that have a net magnetic charge. That is, these particles would have a net north pole or a net south pole, which is very different from an ordinary bar magnet which always has both a north pole and a south pole. These magnetic monopoles are, according to our theories, extraordinarily heavy particles, weighing about 1016 times as much as a proton. In the traditional big bang theory, without inflation, they would have been copiously produced in the early universe. If one assumes a conventional cosmology with typical grand unified theories, one concludes that the mass density of magnetic monopoles would dominate all other contributions by an absurdly large factor of about 1012. Observationally, however, we don't see any sign of these monopoles.

Cosmic inflation provides a simple explanation for what happened to the monopoles: in inflationary models, they can easily be diluted to a negligible density. As long as inflation happens during or after the era of monopole production, the density of monopoles is reduced effectively to zero by the enormous expansion associated with inflation.

The sixth and final reason that I would like to discuss for believing that the universe underwent inflation is the prediction that the theory makes for the detailed structure of the cosmic background radiation. That is, inflation makes very definite predictions not only for the uniformity that we see around us, but it also predicts that there should be small deviations from that uniformity due to quantum uncertainties. The magnitude of these deviations depends on the details of the underlying particle theory, so inflation will not be able to predict the magnitude until we really understand the particle physics of very high energies. However, the shape of the spectrum of these nonuniformities - i.e., the way that the intensity varies with wavelength - depends only slightly on the details of the particle physics. For typical particle theories, inflationary models predict something very close to what is called the Harrison-Zel'dovich, or scale-invariant spectrum. These nonuniformities are viewed as the seeds for the formation of structure in the universe, but they can also be seen directly in the nonuniformities of the cosmic background radiation, at the level of about one part in 100,000. Fig. 1 shows a graph of the recent data from the Boomerang experiment, plotted against a theoretical curve derived for an inflationary model.

Contributed by: Dr. Alan Guth

Cosmic Questions

Eternal Inflation

Evidence for Inflation

 Introduction How Does Inflation Work? Eternal Inflation: Mechanisms Eternal Inflation: Implications Did the Universe Have a Beginning?

Alan Guth

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