Expansion means complexity
and complexity decay.
~Cyril Northcote Parkinson

This is part three of a series on the early universe. In the first article, I described the history of the Big Bang theory and why we believe the universe started in a colossal explosion. In the second article, I described some inconsistencies in the Big Bang theory that need correcting. Now I’ll explain how the theory of cosmic inflation addresses these inconsistencies and why we might believe it in inflation. This explanation will use ideas from quantum mechanics and general relativity; you can find my articles on these subjects here and here.

The Tantalizing Almost-Problems

Last time, I discussed two almost-problems with the Big Bang theory: the horizon problem and the flatness problem.

The horizon problem refers to the strange homogeneity in the cosmic microwave background (or CMB), the light that fills the universe left over from the Big Bang. Light from one end of the universe should not have had time to reach the other end of the universe since time began. However, the CMB looks the same no matter where we look–which is very unlikely unless photons on one end of the sky had time to mix with the photons on the other end of the sky.

The flatness problem has to do withgeneral relativity’s prediction that space and time should be curved… even on a universal scale. In fact, at any given time, space forms a curved three-dimensional hypersurface that lives in four-dimensional spacetime. After the Big Bang, the spatial part of the universe should have become more and more curved. However, we can’t observe any curvature at all! This, too, is very unlikely

The reason I call the horizon and flatness problems “almost-problems” is because they don’t indicate inconsistencies in the Big Bang theory with absolute certainty. Given the unmodified Big Bang theory, we could resolve the horizon and flatness problems simply by assuming that we live in a very special, very unlikely universe. But this resolution isn’t very intellectually satisfying. That’s why cosmologists, most notably Alan Guth, Andrei Linde, Andreas Albrecht, and Paul Steinhardt, developed the theory of inflation.

Resolving the Almost-Problems

To resolve the horizon problem, we need opposite sides of the sky to have been close enough to each other in the early universe for light to pass between them, so that they could mix and homogenize. (We call this state of closeness causal contact.) Furthermore, we need them to have stopped causal contact about 13.7 billion years ago, in order for us to be able to observe them slowly re-entering causal contact today.

One way to achieve this would be for the spatial universe to stay relatively static after the Big Bang. The small size of the universe and its lack of change would allow opposite sides of the sky to enter causal contact with each other. After mass and energy across the universe had sufficiently mixed, the universe would enter a period of extremely rapid expansion, which we call inflation. The inflationary period would pull objects in the universe apart from each other so quickly that light would no longer be able to pass between them. Thus, they would exit causal contact. (Afterwards, however, the rapid expansion would have needed to stop somehow. I will discuss this necessity shortly.)

This rapid expansion also fixes the flatness problem. For example, both balloons and the planet Earth are round–but when we stand on the Earth, it looks flat. This is because everything appears to be flat if you look close enough. (Side note: this is the principle on which the entire field of differential geometry is based!) And we’re very small compared to the Earth. In other words, we’re looking at it very closely–from the viewpoint of our tiny heights, which is measured on a scale of mere meters. Similarly, as space expands rapidly during the inflationary period, it appears larger and larger compared to us. Thus, it appears flat.

 Engineering Inflation

But how could the universe expand like that? And if it did, why isn’t it still expanding? We need a way in which the universe enters a period of rapid inflation and then leaves it. To understand how this might occur, cosmologists take a hint from a current mystery: dark energy.

Currently, the universe is expanding at an ever-increasing rate. It’s not expanding as quickly as in the inflationary period, but if trends continue, it will eventually accelerate to inflationary rates. We don’t know what’s causing this acceleration—it’s possible that the physics on the subject is simply wrong—but one thing that could cause it is a particle with negative energy. With some weird quantum exceptions, we don’t observe any negative energy now, but it’s possible that such a particle existed in the early universe. Indeed, it’s possible that the sign of the energy of the particle changed over time. We call this particle the inflaton.

In the hot, dense early universe, the inflaton filled the universe–and while the universe was static, inflatons from one end of the universe had a chance to interact with the other end, so that the universe because homogeneous. After enough time, the inflaton’s energy became negative, causing the universe to expand. (Indeed, the high density of inflatons would have caused extremely rapid expansion.) Eventually, the energy flipped sign again and inflation stopped. The inflatons then slowly disappeared through a number of processes (like particle collisions) and transferred all their energy into the curvature of spacetime, mass, and light. This process is called reheating, which appears to us as the Big Bang. The energy from the inflatons that went into light became the Cosmic Microwave Background.

But does this mean that we didn’t have a real Big Bang? That inflation only makes it appear as if we had one? Well, we don’t know for sure. Inflation erases all evidence of itself and of what happened before the inflationary period. The shape of the universe before inflation is spread out across the current universe beyond what we can see. In fact, because the universe is still expanding at an increasing rate, there are places in the universe we will never observe. Personally, I do believe there was a Big Bang before inflation. It is at least one very compelling story for the beginning of the universe.

(Some sticky technical details: the inflaton energy is based on the slope of the curve representing its potential energy as a function of the quantum field. Most theories of inflation, such as slow-roll inflation, posit some potential energy curve such that the inflaton only looks like dark energy. Eventually the slope changes and the inflaton becomes much less exotic.)

Quantum Fluctuations And The Seeds of Galaxies

Like electrons today, the inflaton was a quantum particle. And, like all quantum particles today, the inflaton sometimes appeared and disappeared at random throughout the universe. These quantum fluctuations have far-reaching consequences today. Say that in the small early universe, a few million new inflaton particle appeared in a single place. If the universe were static, this wouldn’t matter. The inflatons would spread out naturally and, over time, the inflatons would be equally dense everywhere.

However, in the period of rapid expansion, the new inflatons (which couldn’t travel faster than light) may have been unable to reach other parts of the universe. Indeed, if the inflation were rapid enough, the inflatons at one end of the pocket of high density may not have been able to reach the inflatons at the other end of the pocket. The space between them might have been simply increasing too fast.

Eventually, inflation stopped, and the inflatons disappeared and transferred their energy to other particles or to the fabric of spacetime itself. But this means that the low-density pockets of inflatons would have transferred significantly less energy than the high-density pockets. These early quantum fluctuations in the inflaton density would have later become quantum fluctuations in the cosmic microwave background and in the density of mass itself. Thus, these high-density inflaton pockets must have been the seeds from which galaxies were formed!

But what about the energy that became the CMB? Are there quantum fluctuations there, too? There sure are! Although the CMB is homogeneous almost everywhere, there are tiny little fluctuations in the temperature of the CMB. And these fluctuations line up exactly with the predictions of cosmic inflation! This is the real triumph of cosmic inflation as a theory, and why most of the scientific community now believes it.

Just recently, the Planck collaboration released the results of its four-year study of the CMB. This work refines the early work by the 11-year WMAP survey. The above image shows quantum fluctuations in the temperature of the CMB. The oval is the observable sky; orange represents higher temperature and blue represents lower temperature. (The scale is blown up so that contrast between high and low temperature is obvious, but the difference is actually only about one part in one hundred thousand.) This single image–or more accurately, the earlier WMAP image–is what convinced the majority of cosmologists that inflation might be true.

The Verdict and the Controversey

Through an incredible theoretical and experimental effort, cosmic inflation is slowly becoming a real theory with predictive power. Most astrophysicists, myself included, think that it’s pretty plausible. However, the verdict is still out as to whether or not it’s correct. There are a number of competing theories. Perhaps the most prominent one is the anthropic principle. The idea is that only a universe as flat and homogeneous as ours could support life…so the one we exist in must have these absurdly unlikely properties, or else we wouldn’t be here asking these questions.

There are also a number of competing theories of inflation, mostly having to do with how inflation stopped. Slow-roll inflation predicts that the sign of the inflaton deterministically switched. However, there are other possibilities. For instance, eternal inflation argues that inflation never stopped on the cosmic scale. Instead, because of quantum fluctuations in the density and energy of inflatons, certain bubbles of stability—called bubble universes—appear in the universe where inflation just happened to slow down or stop. (We would live in one of these bubble universes.) These bubble universes would remain relatively static compared to the inflating universe around them, thus obeying the expansion pattern predicted by the Big Bang theory. However, the non-stable parts of the universe surrounding these bubbles would continue to inflate, causing the bubbles to move away from each other. Eventually, the universe would begin to look like Swiss cheese, where the holes are bubble universes.

Questions? Comments? Insults?

Cosmic inflation is pretty complicated and I don’t have as strong a grasp on it as I would like. If I’ve made a mistake, please let me know! (If you want more explanation or have insults or kudos for me, let me know that, too! Thanks as always for reading!