# 11.7 Evolution of the early universe  (Page 5/10)

 Page 5 / 10 Estimated distribution of matter and energy in the universe. (credit: NASA/WMAP Science Team)

## Summary

• The early universe was hot and dense.
• The universe is isotropic and expanding.
• Cosmic background radiation is evidence for the Big Bang.
• The vast portion of the mass and energy of the universe is not well understood.

## Key equations

 Momentum of a charged particle in a cyclotron $p=0.3Br$ Center-of-mass energy of a colliding beam machine ${W}^{2}=2\left[{E}_{1}{E}_{2}+\left({p}_{1}c\right)\left({p}_{2}c\right)\right]+{\left({m}_{1}{c}^{2}\right)}^{2}+{\left({m}_{2}{c}^{2}\right)}^{2}$ Approximate time for exchange of a virtual particle between two other particles $\text{Δ}t=\frac{h}{E}$ Hubble’s law $v={H}_{0}d$ Cosmological space-time metric $d{s}^{2}={c}^{2}d{t}^{2}-a{\left(t\right)}^{2}d{\text{Σ}}^{2}$

## Conceptual questions

What is meant by a “cosmological model of the early universe?” Briefly describe this model in terms of the four fundamental forces.

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

The observed expansion of the universe and the cosmic background radiation spectrum.

In what sense are we, as Newton once said, “a boy playing on the sea-shore”? Express your answer in terms of the concepts of dark matter and dark energy.

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?

If light slow down, it takes long to reach Earth than expected. We conclude that the object is much closer than it really is. Thus, for every recessional velocity (based on the frequency of light, which we assume is not disturbed by the slowing), the distance is smaller than the “true” value, Hubble’s constant is larger than the “true” value, and the age of the universe is smaller than the “true” value.

In the past, many scientists believed the universe to be infinite. However, if the universe is infinite, then any line of sight should eventually fall on a star’s surface and the night sky should be very bright. How is this paradox resolved in modern cosmology?

Experimental results suggest that a muon decays to an electron and photon. How is this possible?

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

$\begin{array}{c}\text{(a)}\phantom{\rule{0.2em}{0ex}}\text{p}+\stackrel{\text{−}}{\text{p}}\to \text{n}+?\hfill \\ \text{(b)}\phantom{\rule{0.2em}{0ex}}\text{p}+\text{p}\to \text{p}+{\text{Λ}}^{0}+?\hfill \\ \text{(c)}\phantom{\rule{0.2em}{0ex}}{\pi }^{\text{ࢤ}}+\text{p}\to {\text{Σ}}^{\text{−}}+?\hfill \\ \text{(d)}\phantom{\rule{0.2em}{0ex}}{\text{K}}^{\text{−}}+\text{n}\to {\text{Λ}}^{0}+?\hfill \\ \text{(e)}\phantom{\rule{0.2em}{0ex}}{\tau }^{+}\to {\text{e}}^{+}+{\upsilon }_{\text{e}}+?\hfill \\ \text{(f)}\phantom{\rule{0.2em}{0ex}}{\stackrel{\text{−}}{\upsilon }}_{\text{e}}+\text{p}\to \text{n}+?\hfill \end{array}$

a. $\stackrel{\text{−}}{n}$ ; b. ${\text{K}}^{+}$ ; c. ${\text{K}}^{+}$ ; d. ${\pi }^{\text{−}}$ ; e. ${\stackrel{\text{−}}{\nu }}_{\tau };$ f. ${e}^{+}$

Because of energy loss due to synchrotron radiation in the LHC at CERN, only 5.00 MeV is added to the energy of each proton during each revolution around the main ring. How many revolutions are needed to produce 7.00-TeV (7000 GeV) protons, if they are injected with an initial energy of 8.00 GeV?

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.)

When an electron and positron collide at the SLAC facility, they each have 50.0-GeV kinetic energies. What is the total collision energy available, taking into account the annihilation energy? Note that the annihilation energy is insignificant, because the electrons are highly relativistic.

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