PMU199Snotes

Cosmology: A Brief History of Our Universe

Might seemingly disparate forces and particles unify together at ultra-high temperatures characterizing the very early universe? We know similar examples of where this sort of concept operates in terrestrial physics.

Symmetry Breaking

Suppose that we take an iron bar at room temperature and then heat it up. When the iron becomes molten (at and above its melting point), the arrangement of the iron atoms changes. When the iron is solid, each iron atom has a spin that points in a particular direction. If the spins are (largely) aligned then we have a magnet. But when the iron is hot enough to become liquid, the iron atoms are free to move and so the average direction of the iron spins is zero. Each iron atom is a tiny magnet, but on average a blob of molten iron has no overall magnetism. We say that the iron liquid is rotationally symmetric.

Suppose that now we let the iron cool. Spins will freeze into small aligned domains, and alignment of the domains can be encouraged with another magnet. The groundstates of a block of solid iron happen when all the spins point in one unified direction: they have the lowest energy (and all groundstates have identical energy regardless of which direction the magnet points in). The funny thing about one of these groundstates is that it has broken the rotational symmetry: it has picked a direction in which to point! ￼￼

Our iron magnet could equally well have chosen any direction in which to point. Any direction is just as good as any other: all of them cost the same amount of energy. There is a continuous set of possibilities - 360 degrees' worth - and this is what matters for spontaneous symmetry breaking.

Another example of a system with spontaneous symmetry breaking is a perfectly cylindrical pencil balanced right on its very tip. The system in this phase has rotational symmetry about the axis of the pencil. Suppose that we wait. Eventually a small breath of wind will make the pencil fall down. When it falls down it can pick any direction in which to point. Once the pencil falls, the system stops being rotationally symmetric.

ElectroWeak Unification

Shelley Glashow, Abdus Salam and Steven Weinberg won a Nobel Prize for explaining how to unify $SU(2)$ weak and $U(1)$ electromagnetic gauge forces together from a theoretical perspective. It was a tour de force: they managed in one fell swoop to explain (a) generation of masses for leptons and quarks (b) generation of masses for W+,W-,Z boson and (c) unify two forces. The technical underpinnings of the Higgs mechanism in the Standard Model are complicated, and I am currently teaching them in my PHY2404S graduate course "Quantum Field Theory II". But the basic concepts can be distilled down to the essential bits pretty easily. Here is the approximate picture.

At high temperature, such as would have been available right after the Big Bang, the idea is that the W+, W-, Z and photon messenger bosons are all massless and are unified into one combination gauge field for the combination $SU(2)\times U(1)$ symmetry. By contrast, at low temperature (such as the ambient temperature of our Universe now) the W+,W- and Z get fat but the photon does not. The W+,W-,Z weak messenger bosons get fat by eating one mode of the Higgs boson. In the process, the $SU(2)$ force is broken away from the $U(1)$ force.

Discovery of the W+,W-,Z bosons in 1983 at the LEP experiment at CERN provided striking confirmation of the Glashow-Salam-Weinberg theory. The LEP machine used to live in the same tunnels currently used now for the LHC. At the time, the collider was running counterrotating beams of electrons and positrons to create the most forceful collisions available in the lab.

The Higgs Mechanism

You might wonder how the symmetry breaking mechanism works for electroweak physics. The name physicists give this is the Higgs mechanism. How does it work? The answer to this is complicated technically, in that I will be teaching it in my graduate PHY2404S course in a week or two! But the basic idea behind Higgsing can be visualized with the aid of a theoretical tool called the Mexican hat (sombrero) potential. This draws a picture of the (potential) energy tied up in the Higgs field, drawn as a function of how big the field is. The figure below graphs this partially: what it describes explicitly is the lowest-energy part of the potential energy story; the brim of the hat actually continues upwards and upwards but this is suppressed in the figure to make the bump visible. In other words, this is a cutaway. The height of the surface tells you the potential energy; how far away the surface is from the middle tells you how big the Higgs field is. ￼

At very high temperatures, the size of the bump in the sombrero is insignificant. The Higgs field basically stays close to the centre, in order to minimize the energy cost. But when the universe cools down, eventually the bump becomes really important compared to the size of your energy budget. As the universe cools more, the Higgs ends up balanced at the top of the bump, and eventually, the only way the energy can be decreased is for the Higgs to fall off the bump down into the valley that corresponds to the brim of the hat. The key point is that to lower its energy, the Higgs has to switch from being in a rotationally symmetric position (at the middle of the bump) to a rotationally asymmetric position (somewhere in the valley). This breaks the symmetry. This choosing of a particular direction in which to fall is what lets the Higgs break the $U(1)$ of electromagnetism away from the $SU(2)$ of the weak nuclear force.

The overall lesson is that a system possessing symmetry at high energy may not possess that symmetry at low energy.

￼Cartoon Summary of Our Origins

￼Note: the Flying Spaghetti Monster is the deity of the Pastafarian religion. To see more details about this religion (created by a pissed-off science student) visit venganza.org.

Let us now look at each of the epochs of the evolution of the universe since the Big Bang.

Planck Epoch (speculative)

In this incredibly intense phase of the universe, gravity and everything else is wildly quantum mechanical. Things that are extraordinarily unlikely in our current epoch happen all the time up at the Planck scale - all the wildest things you can possibly imagine are all going on at once. Smooth spacetime is utterly impractical, as ambient energy makes any graviton scatter very strongly off any other graviton. Temperatures are so high that forces unify, matter and force merge, quarks and leptons unify... into strings(?). Experimentally we have no direct evidence of what happened in this epoch, and we may never know. Part of the problem is that to tease apart all the aspects of Planck-scale physics we would need to be able to experiment on lots of different types of universes. But as observers living where we do, we only have ONE universe to experiment on to learn things. So we may never know what goes on in the Planck epoch because of the limitations of physics itself.

Inflation (speculative)

In this phase, the whole early universe underwent a super-accelerated expansion. The universe grew stupendously during this inflationary epoch: by a factor of thirty orders of magnitude. Causality is not broken by this extremely fast expansion: there are no observers in the early universe who could see superluminal effects. It is only the fabric of spacetime that grew so fast. The physical utility of inflation is that it explains a number of puzzles about the universe: homogeneity, flatness, lack of monopoles, and the horizon problem. It is not necessary for us to get into the nitty gritty details of each of these, but if you expand a little on these topics in your essay it will impress me. There are actually lots of different inflation models that differ in detail. Most of them rely on the dynamics of a quantum field (or fields) with spin zero known as the inflaton. At the end of inflation, reheating fills the universe with radiation (photons) and matter.

Baryogenesis ($10^{-11}$ seconds)

In the beginning, strings and anti-strings (or particles and anti-particles, according to taste) were as numerous as each other. But once the universe cooled down far enough, matter began to outnumber antimatter. This was a very small fractional difference, but it turned out to be crucial for us to exist! From a theory perspective, the hard thing is to explain the details of how this matter/antimatter asymmetry arose. Explaining baryogenesis requires physics beyond the Standard Model (BSM). The jury is still out regarding which theory is right. The LHC should teach us more about this.

Electroweak Symmetry Breaking ($10^{-10}$ seconds)

Above the electroweak temperature, the electromagnetic force is indistinguishable from the weak nuclear force. The Ws and Z and photon are all massless in the very early universe. Below the electroweak temperature, crystallization upon cooling happened differently for the electromagnetic and weak nuclear forces. The Higgs mechanism only gave mass to the weak vector bosons, and not to the photon. ￼￼The above figure is a cartoon of how the various forces split off from each other and at what temperature. (Note: I put Calvin in there from Calvin and Hobbes because his cartoonist made up an awesome name for the Big Bang: The Horrendous Space Kablooie.)

Colour Confinement ($10^{-4}$ seconds)

Above the confinement temperature, quarks antiquarks and gluons were free to roam and mess about interacting weakly. Below the confinement temperature, all quarks and gluons (every single one of them everywhere!) have to be strongly bound together into colourless hadrons: mesons (quark-antiquark) or baryons (colourless combos of three quarks) or colourless glueballs. ￼

Proton/Neutron Ratio (1 second)

Since protons and neutrons are far heavier than their electroweak cousins (electrons, mus, taus and their respective neutrinos), they get affected first by a lowered temperature. The reason is that when you have a limited energy budget making heavier particles becomes harder to do because each of them is so expensive: it requires mc² of energy which might not be easily available. Now, at low temperature, protons are stable, even outside the nucleus. Free neutrons, on the other hand, are not stable: they decay in an average of a bit under 15 minutes. Free neutrons (i.e., those not bound up stably in atomic nuclei) decay into a proton, an electron, and an electron antineutrino. What this implies is that turning a proton into a (heavier) neutron requires energy while the reverse process does not. The lack of symmetry in this regard resulted in a p/n ratio of about 7.

Big Bang Nucleosynthesis (100 seconds)

Nuclear forces are short-range. The proton and neutron won't stick together to make deuterium (or anything else) unless they can get really close. At higher temperatures they simply race around too quickly to form nuclei. But after the universe has become cool enough, nucleons (protons and neutrons) do get close enough to bind, and they can then coexist inside the nucleus. The details of all this are complicated technically but conceptually straightforward. During BBN, no heavy elements were made. Only H, a bit of He, and a teeny bit of Li got made in this epoch. Then where, you might ask, do all the heavier elements come from, like carbon C, nitrogen N, oxygen O, and phosphorus P, which we need for carbon-based biological life forms? They were actually created in stars -- in the process of fusion in both small and large stars and in dying-star explosions known as supernovae. We are, literally, star stuff. In particular, every one of the molecules of your body is made of star stuff. We all are. Isn’t that amazing and wonderful and deep and connecting?

Matter Domination (70,000 years)

Radiation dilutes fast as the universe expands. Matter doesn’t get diluted by expansion of the fabric of spacetime as quickly, because some of its energy is locked up in the rest energy. Radiation gets so diluted that by about 70,000 years photons interact with electrons/positrons much less frequently than they interact with other photons. In other words, the photons have thermalized. They start behaving like radiation that comes from a blackbody, an almost perfect radiator. In fact, the radiation left behind after the Big Bang -- known as the Cosmic Microwave Background Radiation (CMBR) -- is the most perfect blackbody known to humankind. It has a temperature currently of about three degrees Kelvin above absolute zero. This is in the microwave part of the spectrum, near the border with infrared.

Recombination (370,000 years)

Finally the universe got cool enough that electrons could happily fall into orbit around nuclei. The universe is electrically neutral on average (unlike gravity, which has no analog of a negative charge). After about half a million years after the Big Bang, any remaining photons can go about their business sailing about the universe without electromagnetic interference from electrons/positrons. These are the photons that astronomers catch in their various telescopes, ground-based and satellite-based. Now, if we look further back in time, we are seeking older light. The rub is that faraway sources are fainter. Star Formation (1,000,000,000 years) Gravity forces, while weak between any two subatomic particles, can get strong enough for almost anything when you get enough energy/mass together. If you wait long enough, the energy locked up in matter (mostly in hydrogen) sources gravitational attractions, which help clump the matter. Eventually, dense enough regions form to allow the first stars to ignite -- via nuclear fusion.

The above is a composite picture of the Milky Way galaxy produced by the ESO (European Southern Observatory). Isn’t it beautiful? I don’t know about you, but I find cosmology at least as beautiful as the most amazing artworks I’ve ever seen.