THE EXPANDING UNIVERSE

Cosmology Primer: The Expanding Universe

In thinking about the expanding universe, it is tempting to appeal to some sort of simile: distant galaxies are like raisins in a baking loaf of bread, or dots drawn on the surface of a balloon. But the universe is a unique place, and similes tend not to do it justice (or worse, to suggest something misleading). It's actually best just to think about the universe itself, and what it looks like.

So imagine standing outside on a clear night and looking into the sky. Imagine further that you have perfect vision, including not only ordinary light but all other kinds of radiation (radio waves, infrared and ultraviolet light, X-rays and gamma-rays). The first thing you notice are stars; each star is much like our Sun, but further away and correspondingly fainter. But the stars aren't distributed equally throughout the sky; they are arranged into a disk, and our solar system is near one edge of the disk. This disk of stars, orbiting slowly under their mutual gravitational attraction, is our galaxy, the Milky Way. There are almost one trillion stars in the Milky Way; in the night sky it shows up as a faint band stretching from one horizon to the other.

But stars aren't the only thing we see; there are tiny patches of fuzzy light, which stand out in contrast to the pointlike stars. The patches are "nebulae", and were a source of controversy earlier in the twentieth century -- were they clouds of gas and dust within our galaxy, or separate galaxies in their own right? Eventually Edwin Hubble showed that many (although not all) of the nebulae were in fact distant systems of stars, comparable in size to our own Milky Way galaxy. In our observable universe, there are approximately one hundred billion such galaxies. For more discussion, see the page on the luminous universe. 

Cosmology, as the study of the entire universe, would be a completely intractable subject if it weren't for one crucially simplifying feature: if we look over large enough distances, the distribution of galaxies is basically the same everywhere. In technical terms, we say that the universe is both "homogeneous" (the same at every point) and "isotropic" the same in every direction). Of course these statements are not strictly true; the center of a galaxy has a higher average density than the space in 

between galaxies. But as we look over larger and larger distances, the deviations from place to place become smaller and smaller; once we are                                                                                                               Galaxy map from the SDSS

considering distances of hundreds of millions of light years and more, the universe looks extremely uniform.

However, although galaxies are spread evenly throughout space, they are not static as a function of time; Hubble's second great discovery is that the universe is expanding. The concept of an expanding universe can be a tricky one, so it is worth being careful about what we mean. It is best to think of space itself stretching, so that the amount of space between any two distant galaxies is increasing. The observable phenomenon that leads us to this conclusion is the redshift: as light travels from one galaxy to another, its wavelength is stretched as the universe expands, reaching the second galaxy having been shifted to the red (longer wavelengths). We therefore see relatively nearby galaxies slightly redshifted, and very distant galaxies extremely redshifted. The cosmological redshift is similar in result (although different in underlying cause) to the well-known Doppler shift that results when an object is moving away from you. It is therefore convenient to assign a "velocity" to this redshift; Hubble's Law states that this apparent velocity is directly proportional to the distance to the galaxy, with the constant of proportionality being the Hubble constant. (At a deep level, the expansion of space is different than the motion of objects through a static space; however, the differences are negligible when the apparent velocities are much less than the speed of light, so the abuse of language is acceptable.)

Since we see distant galaxies moving away from us, it is tempting to think that we are in the center of something big. But that's an incorrect impression; if we were living on any one of the other galaxies, we would still see all the galaxies moving directly away from us, as a consequence of the general expansion. There is no center to the universe, nor any preferred location; it's basically the same everywhere. Likewise, the universe is not (so far as we know) expanding "into" anything; it's just that the amount of space in our single universe is growing with time.

Einstein's general theory of relativity, which states that spacetime is curved and that curvature is what we perceive as "gravity," provides a dynamical framework for understanding the expansion of the universe. In cosmology, the curvature of spacetime comes from two contributions: the curvature of space by itself, and the expansion rate of the universe. The curvature of space is the same throughout space, and can be positive, negative, or zero; recent observations of the Cosmic Microwave Background indicate that it is close to zero. General relativity then relates the expansion rate and spatial curvature to the energy density of the universe -- the amount of energy in each volume of space. If we know the spatial curvature, and we know the energy density, and we know how the energy density changes as the universe expands, we can reconstruct the entire expansion history of the universe.

In particular, we can extrapolate backwards from our current situation to describe the very early universe. Since it is expanding now, it was smaller in the past; galaxies were closer together, and the universe was both hotter and more dense. Going back sufficiently far, the universe was so hot that galaxies and stars could not exist; further back, individual atoms could not exist; further still, it was too hot for atomic nuclei themselves to exist. If we extend ourselves fearlessly all the way back, the universe was of essentially zero size about 13.7 billion years ago -- the Big Bang. Of course there is a lot we don't know about this period, although there is some that we do; see the pages on the early universe and the really early universe for details.

If we can extrapolate into the past, we can also extrapolate into the future. The problem there, of course, is that we have no observational data to check our speculations. Strictly speaking, therefore, we really don't know what the far future history of the universe will bring. Our best current models, in which the universe is dominated by dark matter and dark energy, predict that it is likely for the universe to continue expanding forever, becoming increasingly cold and dark as time goes by. See the page on the dark universe for more specifics. However, our current ideas are still speculative, so it pays to keep an open mind.

THE EARLY UNIVERSE

Cosmology Primer:The Early Universe

We have no direct knowledge of what the universe was like before the Big-Bang nucleosynthesis era, when the universe was between a few seconds and a few minutes old . It is worth emphasizing that any ideas we have about earlier times are only that ideas. Nevertheless, just as we can successfully extrapolate the laws of physics from the present day back to the time of nucleosynthesis, we may also extrapolate these laws even further back, to construct a picture of what the very early universe may have been like.

In a universe dominated by matter and radiation (as opposed to dark energy), the mutual gravitational pull of all the particles tends to slow down the expansion rate as the universe expands. When the universe was smaller and more dense, it therefore follows that the expansion rate was much larger than it is today. Indeed, as we extrapolate the universe further back in time, we reach a point where the density, temperature, and expansion rate were all infinitely large. This point is a singularity, which we refer to as the Big Bang (although that term is also used for the entire cosmological model that includes the later universe as well). At the Big Bang, our knowledge of what happens gives out; the fact that physical quantities become infinite is a sign that we don't know what is going on. Presumably, in the real world there is no singularity; instead, something happens that cannot be described by physics as we currently understand it.

Just because we don't understand the Big Bang itself doesn't mean we can't usefully talk about the period immediately afterwards, when the universe was in a hot, dense, rapidly expanding state. In the absence of a sensible theory of the origin of the universe, cosmologists ask what initial conditions are necessary to explain the observed features of our universe today. But in fact we want more than that; we would like to believe that these initial conditions are somehow natural, rather than arbitrarily finely-tuned. This desire may or may not be accommodated by reality, but has led to a great deal of interesting speculation about the very early universe.

One puzzle we have about the universe is the apparent dominance of matter over antimatter. Every type of elementary particle (electrons, protons, neutrons, and so on) has a corresponding type of antiparticle (positrons, antiprotons, antineutrons) of equal mass and opposite electric charge. But what we observe in the universe is overwhelmingly matter and not antimatter, which we know because matter and antimatter tend to explosively annihilate when they come into contact with each other. If other galaxies, for example, were made of antimatter, there would be regions in between where particles would intermix, giving rise to high-energy radiation that has not been detected. It is possible that this asymmetry between matter and antimatter is simply a feature of the initial conditions of the universe, but it would seem more satisfying if we could explain how it arose dynamically as the universe evolved. Such a hypothetical process is known as "baryogenesis," since the observed imbalance between matter and antimatter is actually an imbalance between baryons (protons and neutrons) and antibaryons. There are numerous models of baryogenesis, many of which may be testable at upcoming particle accelerators; to date, however, no single model has proven so successful that it has been accepted as a standard picture.

overdense regions collapse to form stars and galaxies. But the finite speed of light makes the situation even more surprising. The CMB shows us what the universe was like 370,000 years after the Big Bang. But when we observe widely separated parts of the CMB, we are seeing regions of the universe that were much more than 370,000 light-years apart at that time. In other words, there was not enough time for any signal to travel from one region to another. So how do these separated regions know that they should be at the same temperature? This conundrum is known as the "horizon problem," since the finite distance light can travel since the Big Bang defines an horizon around each point, and the horizons of distant parts of the microwave sky do not overlap.

Unlike the puzzle of the baryon asymmetry, the horizon problem does have a popular solution -- the idea of inflation. One way of thinking of inflation is to simply imagine that the very early universe went through a period where it was temporarily dominated by an extremely large amount of dark energy, which then suddenly decayed into ordinary matter and radiation. This inflationary dark energy caused the universe to accelerate at a fantastic rate, taking nearby points and moving them very far apart -- so that the widely-separated regions we observe in the CMB were actually quite nearby and in contact early on. This elegant solution to the horizon problem comes along with extra benefits. For one thing, the process of inflation takes any initial curvature of space and diminishes it to near zero, explaining the observed flatness of the universe. For another, inflation wipes out any particles that may have existed before inflation began, which is useful if we don't observe those particles today. An example is provided by "magnetic monopoles," which some theories of particle physics predict should exist in copious amounts, even though none has ever been detected. The desire to get rid of magnetic monopoles was actually the original motivation that led to the invention of inflation by Alan Guth in 1980.

Inflation has another unanticipated benefit: it provides a possible origin of the primordial density perturbations that lead to temperature anisotropies in the CMB and ultimately grow into the large-scale structure we observe today. This phenomenon arises from considering inflation in the context of quantum mechanics. Modern physicists understand that classical mechanics, in which particles have definite positions and velocities, is only an approximation to quantum mechanics, in which such quantities are subject to a certain irreducible uncertainty. The same thing holds true for the density of an expanding universe. Thus, while inflation does its best to make the universe absolutely uniform, quantum mechanics prohibits it from doing so; there is always a small amount of fluctuation in the amount of energy from place to place that no amount of inflation can erase. Indeed, we can use the rules of quantum mechanics to predict what kinds of fluctuations should arise from inflation. The result is a set of perturbations of approximately equal strength at all distance scales. As mentioned in the page on the early universe, these are precisely the kind of fluctuations needed to explain what we observe in anisotropies of the CMB. This doesn't mean that inflation is necessarily correct, but certainly provides some evidence in its favor.

But there remains a great deal that we don't understand about inflation. In particular, while the general framework remains attractive, no specific model of inflation has become popular. In other words, we don't know exactly what this mysterious dark energy was that dominated the universe at very early times, nor how it converted into ordinary matter and radiation. A possible clue could come from another prediction of inflation: gravitational waves. Just as quantum mechanics predicts irreducible fluctuations in the density of matter during inflation, it also predicts fluctuations in the gravitational field, which manifest themselves as gravitational waves. These waves can lead to a specific unmistakable signature in the polarization of the microwave background. Unfortunately, we don't know for sure how strong these gravitational waves will be, and they might be so weak as to be undetectable. But cosmologists are planning experiments to look for them, and if they are detected it will be a great triumph for inflation.

In a sense, inflation hides from view anything that came before it. Nevertheless, we are still curious about the very origin of the universe, and the conditions that gave rise to inflation (if indeed it happened). Presumably any sensible description of this epoch will involve quantum gravity (the long sought-after reconciliation of quantum mechanics with Einstein's general relativity), and perhaps require an understanding of more esoteric physics such as superstring theory.