Astronomy 162: Professor Barbara Ryden

# THE VERY EARLY UNIVERSE

``Though a good deal is too strange to be believed, nothing is too strange to have happened.'' - Thomas Hardy

## Key Concepts

• Horizon problem: Why is the universe so smooth on large scales?
• Flatness problem: Why is the density so close to the critical density?
• These problems are solved if the early universe underwent a period of inflation.

#### (1) Horizon problem: Why is the universe so smooth on large scales?

The temperature of the Cosmic Microwave Background (CMB) is very nearly isotropic. That is, when you look at different patches of the CMB, their temperatures are the same to within 1 part in 10,000. This implies that when the universe became transparent (about 300,000 years after the Big Bang), it was very nearly homogeneous. The homogeneity, or smoothness, of the universe is referred to by cosmologists as the horizon problem.

So why is the homogeneity of the universe such a problem? And why is it called a ``horizon'' problem? What does the cosmic particle horizon got to do with it? Well, remember that when we look at the Cosmic Microwave Background, we are actually looking at the surface of the ionized opaque ``fog'' that filled the early universe. Because the universe became transparent early in its history, long before the present day, the distance to the opaque ``fog bank'' is nearly equal to the our cosmic particle horizon distance. (Our horizon distance is roughly 14 billion light-years; the distance to the opaque ``fog'' is 99 percent of that value.)

Consider two antipodal points on the sky, as far apart as they can be on the celestial sphere. Let's call them point A and point B.

• CMB photons from point A have traveled a distance equal to 0.99 times the horizon distance in order to reach us.
• CMB photons from point B have also traveled a distance equal to 0.99 times the horizon distance in order to reach us.
• Since A and B are in opposite directions as seen by us, the distance from A to B is 0.99 + 0.99 = 1.98 times the horizon distance.
What does this mean? Points A and B are separated by a distance larger than the horizon distance. Hence, they are outside each other's cosmic particle horizon, and are utterly unaware of each other's existence. Despite their lack of communication, they have the same temperature to better than one part in 10,000. Is their extreme similarity in temperature just a coincidence? Or did something happen in the early universe that permitted points A and B to reach the same temperature?

#### (2) Flatness problem: Why is the density so close to the critical density?

The density of the universe divided by the critical density is a dimensionless number that is usually called the density parameter, and is symbolized by the Greek letter Omega. At the present moment, the density parameter is very nearly equal to one, and thus the universe is very nearly flat. The current best limits on Omega tell us that
0.9 < Omega < 1.1
That is, the density of the universe is within 10 percent of the critical density. Why should this be? There's no law of physics that forbids the density to be a million times the critical density, or one-millionth the critical density. The coincidence between the actual density and the critical density looks even fishier when you consider that any deviations of the density and the critical density tend to grow with time while the universe is dominated by light or by matter. Today,
0.9 < Omega < 1.1
At t = 2500 years, when the universe became dominated by matter,
0.9999 < Omega < 1.0001
At t = 10-43 seconds, the earliest time that our knowledge of physics permits us to contemplate,
0.9999999999999999999999999999999999999999999999999999999999999999 < Omega < 1.0000000000000000000000000000000000000000000000000000000000000001
In other words, in order to be relatively flat today, the universe had to be fanatically flat during its earliest stages. Why? Was it just coincidence, or did something happen in the early universe that flattened it out?

Before the year 1980, cosmologists were baffled by the horizon problem and the flatness problem. They shrugged their shoulders and said, ``The universe is fairly homogeneous and flat today because it started out extremely homogeneous and flat. We don't know why it was homogeneous and flat, it just was.'' In 1980, a cosmologist named Alan Guth proposed that the universe became homogeneous and flat because it underwent a very early period of inflation.

#### (3) These problems are solved if the early universe underwent a period of inflation.

Inflation (at least in a cosmological context) can be defined as a brief period of highly accelerated expansion, early in the history of the universe. [According to current models of particle physics, it's likely that inflation began at t = 10-36 seconds after the Big Bang, and lasted for a time t = 10-34 seconds. During this extremely brief interval, inflation caused expansion by a factor of 1050 or so. The idea of inflation (expansion by a factor of 100 trillion trillion trillion trillion during a time of only 100 trillionths of a trillionth of a trillionth of a second) is mind-bending. Nevertheless, inflation provides a welcome solution to the horizon problem and the flatness problem.

How does rapid inflation during the early universe solve the horizon problem? To illustrate, consider our observable universe (that is, the entire chunk of the universe that is bounded by the opaque ionized ``fog''). The current radius of the observable universe is 14 billion light years. At the end of inflation, the radius of the observable universe was a mere 3 x 10-9 light-seconds (about a yard). Think of it! Everything that we can see -- including all the mass of 100 billion galaxies -- squeezed into a sphere that you could span with your arms. But, as Al Jolson once said, you ain't heard nothing yet, folks. Because inflation caused expansion by a factor of 1050 or so, before inflation pumped up the observable universe, it was a mere 3 x 10-59 light-seconds across. Note that at the start of inflation, the horizon size was 10-36 light-seconds, far larger than the minuscule patch that was fated to grow into the currently observable universe. Thus, point A and point B (and every other point within our observable universe) had plenty of time, before inflation, to come to the same temperature.

How does rapid inflation during the early universe solve the flatness problem? To illustrate, suppose that the early universe, before inflation, had positive curvature. During inflation, all the distances in the universe increased by a factor of 1050. This meant that the radius of the universe increased as well. If, for instance, the radius of the universe was only one nanometer before inflation (one billionth of a meter), after inflation, it would be 10 trillion trillion trillion light-years. Just as inflating a balloon to larger and larger radii makes a small patch of it look flatter and flatter, so inflating the universe makes the small patch we call the ``observable universe'' look flatter and flatter.

If you've been paying attention, you have noted that the observable universe, during inflation, increased its radius by r = 3 x 10-9 light-seconds during a time span of only t = 10-34 seconds. To do this, the observable universe would have to expand at a rate far, far faster than the speed of light. ``Gasp!'' you may have said to yourself, ``Doesn't that violate the principles of relativity?'' Actually, there's no need to panic. Objects moving through space can't move faster than light with respect to each other. However, when space itself expands, as happens in our Big Bang universe, there's no restriction on its speed.

Prof. Barbara Ryden (ryden@astronomy.ohio-state.edu)

Updated: 2003 Mar 10