Section 7: The Cosmic Serpent
Throughout this unit, we have moved back and forth between two distinct aspects of physics: the very small (particle physics at the shortest distance scales) and the very large (cosmology at the largest observed distances in the universe). One of the peculiar facts about any modification of our theories of particle physics and gravity is that, although we have motivated them by thinking of short-distance physics or high-energy localized scattering, any change in short-distance physics also tends to produce profound changes in our picture of cosmology at the largest distance scales. We call this relationship between the very small and the very large the "cosmic serpent."
Figure 21: Changes in short distance physics—at the Planck scale—can produce profound changes in cosmology, at the largest imaginable distances.
This connection has several different aspects. The most straightforward stems from the Big Bang about 13.7 billion years ago, which created a hot, dense gas of elementary particles, brought into equilibrium with each other by the fundamental interactions, at a temperature that was very likely in excess of the TeV scale (and in most theories, at far higher temperatures). In other words, in the earliest phases of cosmology, nature provided us with the most powerful accelerator yet known that attained energies and densities unheard of in terrestrial experiments. Thus, ascertaining the nature of, and decoding the detailed physics of, the Big Bang, is an exciting task for both particle physicists and cosmologists.
The cosmic microwave background
One very direct test of the Big Bang picture that yields a great deal of information about the early universe is the detection of the relic gas of radiation called the cosmic microwave background, or CMB. As the universe cooled after the Big Bang, protons and neutrons bound together to form atomic nuclei in a process called Big Bang nucleosynthesis, then electrons attached to the nuclei to form atoms in a process called recombination. At this time, roughly 390,000 years after the Big Bang, the universe by and large became transparent to photons. Since the charged protons and electrons were suddenly bound in electrically neutral atoms, photons no longer had charged particles to scatter them from their path of motion. Therefore, any photons around at that time freely streamed along their paths from then until today, when we see them as the "surface of last scattering" in our cosmological experiments.
Bell Labs scientists Arno Penzias and Robert Wilson first detected the cosmic microwave background in 1964. Subsequent studies have shown that the detailed thermal properties of the gas of photons are largely consistent with those of a blackbody at a temperature of 2.7 degrees Kelvin, as we will see in Unit 5. The temperature of the CMB has been measured to be quite uniform across the entire sky—wherever you look, the CMB temperature will not vary more than 0.0004 K.
Figure 22: Map of the temperature variations in the cosmic microwave background measured by the WMAP satellite.
Source: © NASA, WMAP Science Team. More info
So, in the cosmic connection between particle physics and cosmology, assumptions about the temperature and interactions of the components of nuclei or atoms translate directly into epochs in cosmic history like nucleosynthesis or recombination, which experimentalists can then test indirectly or probe directly. This promising approach to testing fundamental theory via cosmological observations continues today, with dark matter, dark energy, and the nature of cosmic inflation as its main targets. We will learn more about dark matter in Unit 10 and dark energy in Unit 11. Here, we will attempt to understand inflation.
Let us return to a puzzle that may have occurred to you in the previous section, when we discussed the gas of photons that started to stream through the universe 390,000 years after the Big Bang. Look up in the sky where you are sitting. Now, imagine your counterpart on the opposite side of the Earth doing the same. The microwave photons impinging on your eye and hers have only just reached Earth after their long journey from the surface of last scattering. And yet, the energy distribution (and hence the temperature) of the photons that you see precisely matches what she discovers.
Figure 23: Both sides of the universe look the same, although light could not have traveled from one side to the other.
How is this possible? Normally, for a gas to have similar properties (such as a common temperature) over a given distance, it must have had time for the constituent atoms to have scattered off of each other and to have transferred energy throughout its full volume. However, the microwave photons reaching you and your doppelgänger on the other side of the Earth have come from regions that do not seem to be in causal contact. No photon could have traveled from one to the other according to the naive cosmology that we are imagining. How then could those regions have been in thermal equilibrium? We call this cosmological mystery the "horizon problem."
To grasp the scope of the problem, imagine that you travel billions of light-years into the past, find a distribution of different ovens with different manufacturers, power sources, and other features in the sky; and yet discover that all the ovens are at precisely the same temperature making Baked Alaska. Some causal process must have set up all the ovens and synchronized their temperatures and the ingredients they are cooking. In the case of ovens, we would of course implicate a chef. Cosmologists, who have no obvious room for a cosmic chef, have a more natural explanation: The causal structure of the universe differs from what we assume in our naive cosmology. We must believe that, although we see a universe expanding in a certain way today and can extrapolate that behavior into the past, something drastically different happened in the far enough past.
Figure 24: During the period of inflation, the universe grew by a factor of at least 1025.
Source: © NASA, WMAP Science Team. More info
Cosmic inflation is our leading candidate for that something. Theories of cosmic inflation assert that the universe underwent a tremendously explosive expansion well before the last scattering of photons occurred. The expansion blew up a region of space a few orders of magnitude larger than the Planck scale into the size of a small grapefruit in just a few million Planck times (where a Planck time is 10-44 seconds). During that brief period, the universe expanded by a factor of at least 1025. The inflation would thus spread particles originally in thermal contact in the tiny region a few orders of magnitude larger than the Planck length into a region large enough to be our surface of last scattering. In contrast, extrapolation of the post-Big Bang expansion of the universe into the past would never produce a region small enough for causal contact to be established at the surface of last scattering without violating some other cherished cosmological belief.
Inflation and slow-roll inflation
How does this inflation occur? In general relativity, inflation requires a source of energy density that does not move away as the universe expands. As we will see in Unit 11, simply adding a constant term (a cosmological constant) to Einstein's equations will do the trick. But, the measured value of the present-day expansion rate means the cosmological constant could only have been a tiny, tiny fraction of the energy budget of the universe at the time of the Big Bang. Thus, it had nothing to do with this explosive expansion.
Figure 25: A potential like the one shown above for the inflaton field could have caused inflation.
Source: More info
However, there could have been another source of constant energy density: not exactly a cosmological constant, but something that mimics one well for a brief period of a few million Planck times. This is possible if there is a new elementary particle, the inflaton, and an associated scalar field . The field evolves in time toward its lowest energy state. The energy of at any spacetime point is given by a function called its "potential." If happens to be created in a region where the potential varies extremely slowly, then inflation will proceed. This is quite intuitive; the scalar field living on a very flat region in its potential just adds an approximate constant to the energy density of the universe, mimicking a cosmological constant but with a much larger value of the energy density than today's dark energy. We know that a cosmological constant causes accelerated (in fact, exponential) expansion of the universe.
As inflation happens, will slowly roll in its potential as the universe exponentially expands. Eventually, reaches a region of the potential where this peculiar flatness no longer holds configuration. As it reaches the ground state, its oscillations result in the production of the Standard Model quarks and leptons through weak interactions that couple them to the inflaton. This end of inflation, when the energy stored in the inflation field is dumped into quarks and leptons, is what we know as the Big Bang.
Figure 26: All the Standard Model particles could have been produced by the inflaton oscillating around its ground state like a ball rolling around in a valley.
We can imagine how this works by thinking about a ball rolling slowly on a very flat, broad hilltop. The period of inflation occurs while the ball is meandering along the top. It ends when the ball reaches the edge of the hilltop and starts down the steep portion of the hill. When the ball reaches the valley at the bottom of the hill, it oscillates there for a while, dissipating its remaining energy. However, the classical dynamics of the ball and the voyage of the inflaton differ in at least three important ways. The inflaton's energy density is a constant; it suffuses all of space, as if the universe were filled with balls on hills (and the number of the balls would grow as the universe expands). Because of this, the inflaton sources an exponentially fast expansion of the universe as a whole. Finally, the inflaton lives in a quantum world, and quantum fluctuations during inflation have very important consequences that we will explore in the next section.