Chapter 17: Cosmology

Despite its great success, the big bang model does not explain several important features of the universe. The way scientists improve a theory is by subjecting it to new data and by testing it and pushing its limits. The answer to these puzzles may lie in what happened in the first tiny fraction of a second after the big bang.

Why does the universe have a geometry that is nearly flat? The evidence shows that the density parameter, Ω₀, is in the range 0.2 to 0.3. The observations are sufficiently uncertain that a flat universe (Ω₀ = 1) cannot be ruled out, especially if a component of vacuum energy is included. Microwave background observations also reveal no space curvature. In other words, the universe is within a few percent of being flat. To see why this is remarkable, let us use the analogy of the rocket launch. A flat universe is analogous to a rocket that is launched with a velocity of exactly 11 km/s, where the rocket leaves Earth but slows smoothly to an eventual halt in deep space. Give the rocket a factor of two or three more starting velocity and it will leave Earth easily and speed through space. Give it a factor of two or three less starting velocity and it quickly falls back to Earth. In other words, even a slight change in starting velocity from the special number 11 km/s produces a very different result.

Now we can reverse this argument. Imagine that we find the rocket long after it has left Earth, crawling along at a constantly decelerating rate. We can deduce that it must have had a launch velocity of exactly 11 km/s. Why? Because with a launch velocity even slightly different from 11 km/s the rocket would be somewhere entirely different — either much further out in space or fallen back to Earth long ago. Returning to cosmology, we live in a very old and large universe in which the density parameter is close to one. If the density parameter is close to one now, it must have been exactly one in the very early universe. Calculations show that the universe must have started with a density parameter equal to one with a precision of one part in 10⁵⁹! In terms of the expansion of space, space that is nearly flat now implies space that was exactly flat in the early universe. We must account for the flatness of space — it is not a prediction of the standard big bang model.

Temperature map of the universe, as measured by WMAP. Image of the cosmic microwave background.

Why is the universe so smooth? Now, of course, the universe is lumpy with planets and stars and galaxies. However, we know from the uniformity of the cosmic background radiation that the universe was very smooth 380,000 years after the big bang. The temperature is constant to within 0.007 percent everywhere in space. If we think of the universe as a hot gas, then the gas must have been well mixed. The only way to have a gas in perfect thermal equilibrium — all parts at exactly the same temperature — is for heat to be able to move from one part of the gas to another part.

Space was expanding incredibly quickly soon after the big bang. At the time we see with the microwave background radiation, patches of space were separating at 61c, over sixty times the speed of light. One year after the big bang, the separation speed was 1000c! Regions of space that were close together at the time of the big bang have, after 380,000 years, separated by a distance equal to many times the light-travel time between them. The horizons of these two regions do not intersect, which means that no signal can pass between them. No light or radiation can have traveled between regions of space that are outside each other's horizons, so there is no way they could have equalized their temperatures. Yet widely separated directions in the sky have virtually identical microwave background temperatures. This uniformity thus has no explanation in the standard big bang model.

In 1981, MIT physicist Alan Guth was pondering the unexplained smoothness and flatness of the universe when he came up with the idea of the inflationary universe. In this adjustment to the big bang model, he proposed that the infant universe went through a period of extremely rapid (or exponential) expansion. During the inflationary epoch — the incredibly small iota of time from 10^-35 to 10^-33 seconds after the big bang — the universe expanded in size by forty orders of magnitude. Inflation moved matter that originally was near us (within a few meters) to a position far outside today's observable universe (much more than 20 billion light years). The inflationary model presents us with a cosmos that has been stretched far beyond our horizon. Therefore, the observable universe is probably a tiny fraction of the size of the physical universe. Whatever the power of our largest telescopes, we are consigned to a humble corner of an immense cosmos. Inflation is an audacious idea.

A graphical representation of the expansion of the universe with the inflationary epoch represented as the dramatic expansion of the metricseen on the left.

Inflation increased the size of the universe suddenly and dramatically. In terms of a space-time diagram, regions of space whose horizons are widely separated now were within the same horizon at the end of inflation. In other words, regions of space that are now out of contact with each other were in close contact in the very early universe. So it is no mystery that they share the same temperature. Whatever curvature the universe might have had before the inflationary epoch was stretched out by the prodigious expansion. Imagine a tiny balloon that is rapidly inflated to many times its original size. Any section we choose to explore is almost perfectly flat. The flatness of the universe is no longer a coincidence; it is an inevitable consequence of inflation.

Inflation seems incredible. If this idea is to be anything more than esoteric speculation, inflation must have a physical basis, and the inflationary big bang model must make predictions that can be tested by observation. Inflation predicts that space should be extremely close to flat — in terms of cosmological parameters, that Ω₀ = 1. Current research is consistent with this, adding the contributions of normal matter, dark matter, and dark energy. Inflation also smooths the universe out very effectively, consistent with the flatness of space measured with microwaves from the big bang. The inflationary model predicts that the remaining ripples, which are the seeds from which galaxies grow, must date back to the first tiny fractions of a second after the big bang. The trigger for inflation is hypothesized as a change of state that occurred when three of the four fundamental forces diverged in strength; the era of inflation is so early that the seeds of galaxy formation are quantum fluctuations greatly amplified by exponential expansion.

What would be a "smoking gun" to show that inflation actually happened? The answer could lie in extremely accurate measurements of the microwave background radiation. Inflation predicts that the tiny temperature variations should be imprinted with polarization from gravity waves. The next generation of more precise CMB experiments may be able to detect this signature. To push our understanding of the universe back to within a tiny fraction of a second of the big bang would be an extraordinary achievement.