The Universe in its first second - Weird and Whacky



The Universe in its first 10-43 to 10-11 seconds: Quantum Fluctuations

The physics of the very early Universe is quite unknown. At these early times the Universe was in a very extreme state with a temperature of approximately 1032 K and a density of 1097 grams per cubic centimeter. These are absurd numbers of course and we have no real clue what kind of physics is occurring here nor even what the meaning of "space" is under such extreme conditions. Among the unknowns is whether or not quantum mechanics exists at these early times. If it did, there may have been important consequences whose philosophical nature are like Democritus opined 2500 years ago. One of the fundamental tenets of Quantum Theory is known as the uncertainty principle. One of the variations of this principle tells us that we can never precisely know the energy state of a particular particle and the duration of that energy state. In equation form, this is expressed as

where h is known as Planck's constant and is one of the fundamental constants of nature. This is the same constant that determines the energy of a photon:

While Planck's constant is such a small value that the energy fluctuation equation above has no relevance in the macroscopic world, in the extremely early Universe, the time interval Dt could be arbitrarily small and hence the energy fluctuations DE could have been arbitrarily large. In this sense, the Universe has no choice but to happen as the energy fluctuations which produced it initially were naturally occurring.

We don't know if this is the correct physical explanation or not. On the other hand, these quantum fluctuations in the early Universe certainly allow for the spontaneous creation of very massive hadronic pairs (because the energy levels are so high). Now its most likely that these heavy hadron + heavy anti-hadron particles just annihilated one another. However, there is a possibility that some small residue of very massive hadrons are left over. If so, they could be a major mass constituent in the Universe. These particles would be weakly interacting, meaning that they would not influence the dynamics of the early Universe or decay into smaller mass particles. Weakly interacting massive particles have been given the nickname WIMPs. If they really exist, there may be several of them whizzing through your body as you read this.



The Quark-Gluon Plasma

While physicists are uncertain if WIMPS actually exist or not, there is a similarly strange state in the early Universe that most agree must have existed. When the Universe was very small, the quarks were very close together. Recall that the force between quarks , provided by the gluons, increases with increasing quark separation. When the quarks are very close to one another, the force drops dramatically. In fact, in this early Universe the quarks were so close to one another that no hadrons could exist. Hence, even though U and D quarks were present, they could not form a proton because the quarks cannot be bound together by the gluons and so the quarks had to be "free" in the sense that they were not contained in any hadron. At this point the Universe consists of a sea of high energy photons with individual quarks and gluons floating about.

The basic condition for the free quark era is that the density of the Universe has to be in excess of nuclear densities (1014 grams per cubic centimeter). This condition is fulfilled when the Universe is less than 1 millionth of a second old. After this time, the expansion has lowered the density to below the nuclear density threshold and the quarks can now be assembled into hadrons. After this assembly, conventional physics more or less holds from here on out. Prior to this, the physics of this kind of free quark/gluon plasma is largely unknown.



Unification of the forces

There were other strange attributes of the Universe at this time. Easily the most theoretically spectacular possibility in this very early Universe involves the unification of the forces. For instance, at this time the gravitational force and the strong force have the same amplitude. Why is this so? As you know, the gravitational force law goes as R-2 but at very early times, R is extremely small (smaller than any particle) so the gravitational force is extremely large. This is a very strange physical regime which leads to the following theoretical possibilities:

  • particle creation could come directly from the gravitational field.

  • all of the Universe could be in the form of one particle but that particle would be indistinguishable from the gravitational field of the Universe.

As the Universe is rapidly expanding, R is rapidly increasing and the gravitational energy is going down so that the gravitational force becomes much weaker than the strong force and the two become separate forces. By the end of this era, (10-11 seconds), a similar separation occurs between the electrostatic force and the weak force. Whenever these symmetric forces are decoupled the Universe is said to go through a phase transition. The symmetry breaking is done in a specific manner so that the forces have now separated and are defined by a characteristic ratio of their strengths. This defines the physics of our Universe. Much theoretical research is currently underway to better understand what causes the symmetry breaking and allows the forces to assume their characteristic values. Thus another question we are not allowed to ask is "how come gravity is as weak of force as it is?". We just don't know.



The Matter/Anti-matter Asymmetry

Between 10-11 and 10-2 seconds the Universe continues to cool rapidly. The reaction rate (the conversion of energy into mass and the annihilation of matter anti-matter pairs) was so large that the Universe was governed by a statistical process known as thermodynamic equilibrium. Under conditions of thermodynamic equilibrium the only thing that matters is the temperature. Hence, the conditions at any one time in the early Universe do not depend on the conditions that happened just before that time. The only thing that determines the physics is the temperature at a particular epoch. This is a large simplification which allows us to identify statistical processes that might have been at work.

In so doing, however, we run into another important unknown. Think about it- if the Universe had exactly equal amounts of matter vs anti-matter then it would have totally annihilated itself and the Universe would only consist of photons (energy) and no matter. Yet you are made of matter so what gives? One possible explanation is that some agent in the early Universe acted to separate out the matter and anti-matter into different areas thus preventing interaction and annihilation. However, if that was the case, we would expect to observe entire galaxies made of anti-matter in the same way that we observe galaxies made of matter. No such anti-matter galaxies have ever been detected.

Hence, we are driven to another conclusion which is that there must have been an excess of matter over anti-matter. But how big is this excess? Well, we can measure that directly by comparing the energy density in the microwave background with the matter density in the Universe. This gives us our canonical photon-to-baryon ratio of about 1 billion. So for every one billion anti-quarks that existed in the early Universe, there was 1 billion and one quarks. This small asymmetry is the matter residue that survived the early Universe to produce all the stars, galaxies and observers today. However, this leads to another fundamental question that has no answer yet: what produced this asymmetry and why is it roughly one billion to one, instead of, say, one trillion to one, one million to one, etc, etc? Again, we don't know the physics that produced this exact asymmetry although there have been some suggestions that the particular form of the electro-weak symmetry breaking produced this asymmetry at a preferred value.



Epoch 1: T = 0.01 seconds

At this time the temperature has cooled to about 100 billion degrees and the density has dropped to around 1 billion grams per cubic centimeter. These conditions are still more extreme than that found in any star. The constituents of the Universe at this time are:

  • Protons, neutrons, electrons and neutrinos

  • One billion photons for each proton, neutron, and electron

  • matter and energy exist in thermal equilibrium

At this time the Universe is still so dense that it is opaque to neutrinos. Ordinarily, neutrinos do not easily interact with other forms of matter, however, in cases of high density, the neutrinos can not travel through the matter without interacting. There are two fundamental neutrino interactions which are occurring

anti-neutrino+proton neutron+anti-electron

neutrino + neutron proton + electron

In these two reactions we can see that neutrinos are the mediating agent which allows protons to be converted to neutrons and vice-versa. A good exercise for the student at this point is to verify that the above reactions indeed follow the conservation rules established previously.

The above reactions keeps the number density of protons and the number density of neutrons constant. That is, there is thermal equilibrium between protons and neutrons. This is extremely important and will lead to a testable prediction later. Recall that a free neutron will decay in about 900 seconds (its half-life). At t = 0.01 seconds, none of the neutrons have decayed and furthermore, new neutrons are being made from protons. So, as long as the neutrinos can interact with neutrons and protons, this balance will be kept. Hence the proton-to-neutron ( p/n ) ratio is 1.

Epoch 2: time = 0.11 seconds

The Universe has now cooled to 30 billion degrees but its density has dropped even more, down to around 10 million grams per cubic centimeter (the density of a white dwarf star). Now we see the first change in the p/n. Since neutrons are slightly heavier than protons (by the mass of an electron) then the n --> p cycle in the previous neutrino reaction is favored over the p --> n cycle. So we have a small loss of neutrons which increases p/n to 1.6. Still, the Universe remains in thermal equilibrium between matter and energy but the reaction rate is rapidly slowing down due to expansion and cooling. Soon, no more matter will be created from pair production and then the total amount of matter and energy is fixed forever, in the expanding Universe.