Bucknell Physics 212 Supplement

Section 12.3 Crucial Events of the Early Universe

The universe began some 14 billion years ago with a Big Bang and has been expanding and cooling ever since. Table 12.1 is a list of the crucial events that occurred early on, most of which we will try to explain.

How can we possibly determine when these events occurred? Except for the end of neutrino interactions and the time of quark confinement, each of these events can be understood in terms of the energies available to maintain thermal equilibrium. For instance, the end of the electro-weak unification occurred when the massive gauge bosons of electro-weak theory (the \(W^+\text{,}\) \(W^-\text{,}\) and \(Z^0\)) could no longer be produced in prodigious amounts from random collisions of particles in thermal equilibrium. In other words, as the universe cooled, the ambient thermal energy became insufficient to create such massive particles. When this occurred, the large mass of the \(W\) and \(Z\) differentiated them from the massless photon, the messenger particle of electromagnetic theory. After this time the weak and electromagnetic interactions were observed to behave differently.

So how can we relate the time of the splitting off of the weak interaction to properties of the \(W\)'s and \(Z\)'s? Here's how. The theoretical model for electro-weak unification, the Weinberg-Salam theory of 1973, predicted rest energies for \(W\) and \(Z\) in the range of 80–\(100\Xunits{GeV}\text{.}\) This prediction was dramatically confirmed when the rest energies of \(W\) (\(84\Xunits{GeV}\)) and \(Z\) (\(92\Xunits{GeV}\)) were measured in the process of their experimental discovery at CERN in 1983. If we round these rest energies up to \(E=100\Xunits{GeV}=10^{11}\Xunits{eV}\text{,}\) we can use (12.3) to estimate the time when this much energy was available as ambient thermal energy. We find

as shown in the table. In general, the energy available at the time of all but two of the events above is related either to the rest energy of a particle or to a reaction energy associated with the event. The problems expand on this relationship.

Finally, let's try to explain the remaining two events: the decoupling of neutrinos from thermal equilibrium with the rest of the universe and the confinement of quarks inside hadrons. Both of these events depend on the average density of the universe which, as the universe expands, is continually decreasing.

Using some of the assumptions needed (but not presented here) to derive Eqs. (12.2) and (12.3), along with estimates of the present average density of the universe, we find a density of \(4\times 10^5\Xunits{g/cm ^3 }\) (and thus \(4\times 10^5\) times that of water) for neutrino decoupling and \(4\times 10^{13}\Xunits{g/cm ^3 }\) for quark confinement. Now neutrinos are very penetrating particles. Those produced in modern accelerators can penetrate miles of plate steel with less than one in a million being absorbed! The high energy neutrinos of the early universe were even more penetrating. When the universe's density fell to \(4\times 10^5\Xunits{g/cm ^3 }\text{,}\) the absorption rate of neutrinos (in reactions like \(\nu+p \to n + e^+\)) fell significantly below their production rate, and neutrinos could no longer exchange enough energy with the rest of the universe to maintain thermal equilibrium.

Quark confinement is explained by density considerations in a similar way. Before \(10^{-4}\Xunits{s}\text{,}\) individual quarks were “free” in the sense that they did not travel around through space in groups of quark-quark-quark (baryons) or quark-antiquark (mesons). A single colored quark could go where it pleased. But this was only because the density of the universe was comparable to the density of an atomic nucleus, around \(10^{14}\Xunits{g/cm ^3 }\text{.}\) The entire universe was one big nucleus! As a result, any individual quark was never far from lots of other quarks, and the gluon “rubber band” never had to be stretched to give rise to confining forces. After this time, the density decreased enough that spaces started forming between nucleons and other particles, and quarks became confined inside hadrons in colorless combinations.