Bucknell Physics 212 Supplement

1.

Use the time in Table 12.1 to calculate the rest energy associated with the end of Grand Unification. What particles would have about this mass?

2.

About how long after the Big Bang would there be insufficient energy to create $\mathrm{\Lambda }$-$\bar{\mathrm{\Lambda }}$ pairs? The rest energy of a $\mathrm{\Lambda }$ is $1116\mathrm{MeV}\text{.}$

3.

Assuming that one photon is released in each baryon-antibaryon annihilation, why are there ${10}^9$ photons/baryon after annihilation and not some other number?

4.

What is the thermal energy per particle available at $t=1\mathrm{s}\text{?}$ How does this compare with the combined rest energies of an electron-positron pair? What happens to positrons after this time?

5.

List the types of particles you might expect to find abundantly in the early universe during the following epochs:

1. ${10}^{-10}$ s to ${10}^{-4}$ s after the Big Bang

2. 1 s to 400 s after the Big Bang

3. ${10}^5$ years after the Big Bang

6.

What particle energy is associated with the time of quark confinement? What hadron has about this rest energy?

7.

Use (12.2) to estimate the photon temperature at the present time ($\sim$10–15 billion years after the Bang). Note that this is an overestimate since the assumptions of (12.2) have broken down.

8.

Transition energies for typical atomic states are about 1–$10\mathrm{eV}\text{.}$ That is, photons in this energy range are captured by atoms to excite upward transitions. Use (12.3) to estimate when in the early universe this “capture effect” became energetically impossible.

9.

The $X$ and $\bar{X}$ bosons decay slightly differently because of a small flaw in charge conjugation invariance. Suppose the decay scheme for $X$ had the following branching ratios:

1. Take 3000 random $X$'s and 3000 random $\bar{X}$'s. How many each of quarks, leptons, antiquarks, and antileptons would appear after all $X$'s and $\bar{X}$'s decayed?

2. Let all the quarks combine into baryons, and all the antiquarks combine into antibaryons. How many of each are there?

3. Now let all the particles and antiparticles annihilate as completely as possible. What's left over? Assume one photon is released from each annihilation.

4. Calculate the photon to baryon ratio for this ($X\text{,}$ $\bar{X}$) decay scheme.