Timeline of the Universe

Unification of Forces

There are four known forces in nature: strong nuclear, electromagnetic, weak nuclear, and gravity (in decreasing order of strength with ratios of 1:10^-12:10^-14:10^-40 with ranges of 10^15m, infinity, 10^-17m, infinity respectively). In the late 19th century, James Clerk Maxwell unified the electric and magnetic foreces as aspects of the same phenomenon, electromagnetism. His four equations describe the electric and magnetic forces experienced by charged bodies. Can this be done with all the forces? It is certainly philosophically appealing to think that all the forces of nature are aspects of a single underlying theory!

In our current paradigm for physics, the standard model, as well as most viable alternatives, the forces become unified as the energy of particles undergoing the interactions increases. At high energies, you cannot tell the difference between any of the forces, and it is only at low energies where we experience the universe that the four fundamental forces become distinct. This idea is related to the concept of symmetry in modern physics, since a perfectly "symmetric" universe is one where everying is interchangeable, particles and forces for example. Thus, the forces and particles become differentiated through the mechanism of spontaneous symmetry breaking, which gives particles their different masses (why is the proton more massive than the electron?) and forces their different strengths and couplings to particles (why is the strong force stronger than the weak force?).

The weak force is intermediated by the W and Z particles. The W and Z have measured masses of around 90 GeV (1 GeV = 10^9 electron volts energy equivalent mc^2. Thus, the proton mass is 0.94 GeV.) The neutral Z is slightly heavier than the charged W+ and W-. Thus, at T of about 10^15 K, W and Z bosons can be created and destroyed out of photons, and thus we might expect the electromagnetic force carried by photons and the weak force carried by the W and Z to be indistinguishable. Indeed, at this temperature and higher the electromagnetic and weak forces are unified into the electroweak force. The electroweak theory and unification was verified about 15 years ago in particle accelerator experiments. The electroweak unification occured approximately 10^-12 seconds after the big bang in our model.

Given the success of the electroweak unification theory, we might confidently expect to be able to unify the electroweak and strong nuclear forces at even higher energies. In fact, Einstein himself spend his last years looking for such a grand unified theory or GUT. From the strength and nature of the strong force, we expect that this should occur at energies of 10^14 GeV (10^23 eV) corresponding to temperatures of 10^27 K. Unfortunately, this energy is well above the capabilities of current and projected future accelerators (around 10^12 eV), but there some lower energy aspects of GUTs that can be tested even at these energies. We expect that at temperatures above 10^27 K and higher, which occurs 10^35 seconds and earlier after the big bang, the electro-weak-strong forces are unified, and only gravity stands alone. Also, at this so-called GUT transition when the strong force split off, some theories state that there was a phase in the evolution of the Universe where a cosmological constant dominated - this is the era of inflation described below.

The Planck Era - The Beginning?

To unify the final (?) force, we need to go back even farther to temperatures of 10^32 K at a time 10^-43 seconds after the "big bang"! The energy of this full unification can be estimated by considering what it might mean for photons and gravity to be equivalent. For example, is there an energy where a photon can create a relativistic massive particle that is its own black hole? If we remember what we've done before, we can see that this will occur when the wavelength (h/mc) is equal to the Schwarzschild radius (2Gm/c^2):

At these energies and higher, there will be the creation and destruction of these black hole -like particles. Since we learned from general relativity that gravity means the curvature of space-time, then at these energies and higher, the concept of space and time breaks down! (Is this another sort of unification and symmetry?) In fact, the theory that must describe this will have to put gravity on the quantum mechancial level (since the wavelength of the black hole is equal to its size) - this is called quantum gravity, and this earliest (?) phase of the Universe is known as the Planck Era. Since we have no workable theory of quantum gravity (though there are some intriguing possibilities), we really do not understand the Universe at times earlier than this (of course, it is likely that time as we know it is not relevant in the Planck era). This can in some sense be considered to be the "Big Bang", where in our space-time continuum came into being.

Inflation

As we stated when we began our investigation into cosmology, by and large we seem to live in a Universe that is homogeneous and isotropic. In particular, we look in two very different directions on the sky, we find that the structure of the Universe appears the same. For example, except for the dipole due to our own velocity through space, the cosmic microwave background radiation appears to be isotropic to the level of 1 part in 10^5 or so, even on opposite sides of the sky. The crucial question is: How did the Universe know to make the cosmic background 2.726 K in every direction that we see? This may seem like an unimportant question, or some sort of metaphysics, except for the fact that in our model for the expanding universe, those parts of the universe could never have communicated with each other at the speed of light! Recombination occured about a million years after the big bang, which was some 15 billion years ago - that's how long it took light to reach us from when the microwave background was last scattered and its temperature and fluctuation level imprinted. Thus, it would have taken twice that, or a couple of million years less than twice the present age of the Universe for any information, forces, photons or particles to have interacted between these regions. One of the cornerstones of physics is the concept of causality, that for something to "cause" something else to happen, some interaction must have taken place which occurs at the speed of light at a maximum. Thus, two regions of space have been separated by a distance equal to or less than the light travel time between for the age of the Universe are said to have been in causal contact. Patches of the sky separated by an angular distance of more than 2 degrees were never in causal contact at the time that the microwave background was generated. In general, it is difficult to see how the Universe seems homogeneous and isotropic on scales that were never in causal contact given our expanding universe model.

Of course, it could be solved by resorting to special initial conditions. The subsequent evolution of a system (like the Universe) under physical law is given by the inital conditions to say what we started with and the laws of physics to tell us what happend to them - you should end up with the Universe as we observe it now if you have the right model. Thus, we could put the isotropy of the Universe as we see it down to the assumption that it started out very homogeneous to begin with. However, it is much more satisfying if we have some physical reason that the Universe should appear isotropic, like it were mixed by heat and convection like the atmosphere of a star. But this requires causal contact. The maximum distance which two points in causal contact can be is called the horizon. This is a different sort of horizon from, but related to, the event horizon we encountered when discussing black holes. The problem of causality between two distant part of the observable universe is called the horizon problem.

The solution is to modify the evolution of the Universe to make regions now far apart even closer than they would be under the normal expanding model at very early times. Thus, we need to change the energy equation to allow faster than normal expansion early on. When we discussed the effect of a positive cosmological constant in Einstein's equation, we noted that if the cosmological constant term were large enough, you would get exponential expansion, or inflation of the Universe:

becomes, when the W term dominates

Using v=HR, we find that H is constant H^2 = W, and thus (using calculus) that if R=R0 at t=t0 at some point during inflation, then

For the universe to be as isotropic as we see it and yet purely causal, it turns out that the universe must have inflated by a factor of e^60 or more (10^26 or more).

If you think a bit, however, you should notice a problem in a cosmological constant to drive inflation: how do you stop it? The exponential inflation with H^2=W will go on forever unless we get rid of the W term after the universe has inflated sufficiently. If for some reason W were to drop to zero (or at least much smaller than 2GM/R^3), then the normal Hubble expansion as determined by the density would take over. It turns out that using our standard model for particle physics, there are indeed mechanisms for causing inflation, expanding the Universe by 10^50 or so, then safely turning off inflation. There are some theoretical indications in our theory that this occured at the time of the GUT transition at 10^27 K. The mechanism of inflation is widely, though not universally, accepted among cosmologists as having occured in the very early Universe.

One of the consequences of inflation is that after expanding by such a large amount, the curvature of the Universe at the end of inflation should be very nearly flat. Most cosmologists who calculate inflationary models would say that inflation predicts a Universe that is flat, and thus very nearly the critical density. This solves another problem in cosmology, called the flatness problem. It appears observationally that the universe is at least within a factor of 10 of the critical density, that is that the observed density is 10% or more of the critical density. In the expansion (after inflation) the Universe diverges from the critical density, thus if it is within a factor of 10 now, it had to be nearly the critical density much earlier on. This is another worrisome case that would require fine-tuning of the initial conditions (causality and all that). Inflation leads naturally to a very nearly flat universe. The only problem is that most models of inflation naturally lead to a Universe much closer to the critical density than a factor of 10. Thus, inflation may do too good a job of solving the flatness problem if observations indicating that the current density is only 10%-40% of the critical density. The jury is still out on what our density really is, but this may be a potential problem with the inflationary theory.

Also, more work needs to be done on the details of the exact physical mechanism involved in the inflation (what particles are involved, how long it went on, whether gravity waves were generated). It is interesting that in order to get rid of the cosmological constant W at the end of inflation, it energy which was driving the expansion of space must be turned into something. It turns out it is converted into radiation and particles (thus making the matter-energy density the critical density), and that all the matter and radiation in the universe today was generated from the cosmological constant energy at the end of inflation. All the matter and energy density that was present before inflation was "inflated away" to low densities by the exponential expansion. Kind of cool, eh?

Paul Steinhardt, professor of Physics and Astronomy at Penn, has been a pioneer in the development of the inflationary theory in cosmology. See also the Cosmology and Astrophysics at Penn pgae for a description of this and other cosmological research at the University of Pennsylvania.

Current Problems in Astronomy

We have concentrated on problem solving and derivation of models and quantities because the scientific method relies on the ability to make predictions and test with observations. It is rather remarkable that mathematics serves as the language in which to phrase our questions about the nature of the Universe. In my opinion, this is a "deep" concept, of fundamental philosophical and metaphysical importance. Are there limitations on the ability of mathematics to model the Universe? Food for thought.

The picture I have given you of the Universe should be taken seriously not because it is written in a textbook, but because we can calculate the relevant quantities using the laws of physics, which were in turn built upon a sequence of observations, hypotheses, theories, then further observations.

Steven T. Myers - Last revised 05May96