11.7 Evolution of the Early Universe

Compare the abundance of helium by mass 10,000 years after the Big Bang and now.

Describe two pieces of evidence that support the Big Bang model.

If some unknown cause of redshift—such as light becoming “tired” from traveling long distances through empty space—is discovered, what effect would that have on cosmology?

Each of the following reactions is missing a single particle. Identify the missing particle for each reaction.

$\begin{matrix}(\text{a}) \text{p} + \overset{−}{\text{p}} \rightarrow \text{n} + ? \\ (\text{b}) \text{p} + \text{p} \rightarrow \text{p} + \Lambda^{0} + ? \\ (\text{c}) \pi^{–} + \text{p} \rightarrow \Sigma^{−} + ? \\ (\text{d}) \text{K}^{−} + \text{n} \rightarrow \Lambda^{0} + ? \\ (\text{e}) \tau^{+} \rightarrow \text{e}^{+} + \nu_{\text{e}} + ? \\ (\text{f}) \left(\overset{−}{\nu}\right)_{\text{e}} + \text{p} \rightarrow \text{n} + ?\end{matrix}$

A proton and an antiproton collide head-on, with each having a kinetic energy of 7.00 TeV (such as in the LHC at CERN). How much collision energy is available, taking into account the annihilation of the two masses? (Note that this is not significantly greater than the extremely relativistic kinetic energy.)

The core of a star collapses during a supernova, forming a neutron star. Angular momentum of the core is conserved, so the neutron star spins rapidly. If the initial core radius is $5.0 \times 10^{5} \text{km}$ and it collapses to 10.0 km, find the neutron star’s angular velocity in revolutions per second, given the core’s angular velocity was originally 1 revolution per 30.0 days.

(a) What Hubble constant corresponds to an approximate age of the universe of $10^{10}$ y? To get an approximate value, assume the expansion rate is constant and calculate the speed at which two galaxies must move apart to be separated by 1 Mly (present average galactic separation) in a time of $10^{10}$ y. (b) Similarly, what Hubble constant corresponds to a universe approximately $2 \times 10^{10}$ years old?

The intensity of cosmic ray radiation decreases rapidly with increasing energy, but there are occasionally extremely energetic cosmic rays that create a shower of radiation from all the particles they create by striking a nucleus in the atmosphere. Suppose a cosmic ray particle having an energy of $10^{10} \text{GeV}$ converts its energy into particles with masses averaging $200 \text{MeV}/ c^{2}$.

(a) How many particles are created? (b)…

Plans for an accelerator that produces a secondary beam of K mesons to scatter from nuclei, for the purpose of studying the strong force, call for them to have a kinetic energy of 500 MeV. (a) What would the relativistic quantity $\gamma = \frac{1}{\sqrt{1 - v^{2} / c^{2}}}$ be for these particles? (b) How long would their average lifetime be in the laboratory? (c) How far could they travel in this time?

Assuming a circular orbit for the Sun about the center of the Milky Way Galaxy, calculate its orbital speed using the following information: The mass of the galaxy is equivalent to a single mass $1.5 \times 10^{11}$ times that of the Sun (or $3 \times 10^{41} \text{kg}$), located 30,000 ly away.

(a) A particle and its antiparticle are at rest relative to an observer and annihilate (completely destroying both masses), creating two $\gamma$ rays of equal energy. What is the characteristic $\gamma$-ray energy you would look for if searching for evidence of proton-antiproton annihilation? (The fact that such radiation is rarely observed is evidence that there is very little antimatter in the universe.) (b)…

(a) Use the Heisenberg uncertainty principle to calculate the uncertainty in energy for a corresponding time interval of $10^{−43} \text{s}$. (b) Compare this energy with the $10^{19} \text{GeV}$ unification-of-forces energy and discuss why they are similar.