# Solutions to Problems for Chapter 23

Read Chapter 23, Sections 1, 2, and 3 -- note, we skipped the separation of forces in the early Universe and the resulting burst of expansion called "inflation"

1.) Immediately after the Big Bang, the Universe was:
a.) cooler and less dense than it is now
b.) cooler and more dense than it is now
c.) hotter and less dense than it is now
d.) hotter and more dense than it is now
Answer: "d" hotter and more dense

2.) Very early in the Universe's history, the conditions were right for making matter plus antimatter from:
a.) photons
b.) electrons
c.) the GUT force
d.) magnetic fields

3.) In order to produce 1 electron and 1 antielectron (also called a positron) via the pair production mechanism, how much energy is required?
a.) the energy equal to the mass of an electron times c2
b.) the energy equal to the mass of an antielectron times c2
c.) the energy equal to the mass of an electron times c2 plus the the mass of an antielectron times c2
d.) none of the above
Answer: "c" in order to make both an electron and an antielectron, the required energy is the sum of the mass energies of both the electron and antielectron

4.) In 1 sentence, why did pair production stop (to be more precise, why did the Universe cease to have widespread pair production)?
Answer: Very energetic photons are needed in order to have pair production. But, as the Universe aged, the temperature of the Universe decreased, causing photons with sufficient energy to become rare.

5.) In 1 sentence, why did the annihilation of matter with antimatter stop?
Answer: Annihilation (i.e. matter + antimatter => photons) proceeded until there was no more anti-matter.

6.) Just before the annihilation of matter with antimatter stopped:
a.) There was less matter than antimatter in the Universe
b.) There was the same amount of matter as antimatter in the Universe
c.) There was more matter than antimatter in the Universe
Answer: "c" there was more matter than anti-matter. There must have been more matter than anti-matter in order for some matter to remain after all of the anti-matter had been destroyed via annihilation with matter.

7.) The vast majority of helium atoms that exists in the universe today were made during the Era of Nucleosynthesis, when nuclear reactions were common in the early Universe. How would the universe be different if there had been a smaller ratio of neutrons to protons during this era?
a.) the ratio of helium atoms to hydrogen atoms in the universe today would be smaller
b.) the ratio of helium atoms to hydrogen atoms in the universe today would be larger
Answer: "a", most of the helium atoms in the Universe today were made just after the Big Bang. Each helium required 2 protons and 2 neutrons, so if there were fewer neutrons in the early Universe, there would be fewer helium atoms.

8.) What changed during the Era of Nuclei?
a.) neutral hydrogan atoms stopped breaking apart into protons + electrons
b.) free-floating electrons stopped blocking photons from moving easily through space
c.) both of the above
d.) none of the above
Answer: "c" At the beginning of the Era of Nuclei, the reaction (proton + electron <=> neutral hydrogen atom) could go in either direction (ditto for helium nucleus + 2 electrons <=> neutral helium) and at any given moment, the Universe contained protons, helium nuclei, electrons, neutral hydrogen atoms, and neutral helium atoms. The charged particles were doing a good job of blocking the motion of photons -- photons bounced off of them. But, at the end of the Era of Nuclei, neutral atoms stopped breaking apart and so stopped freeing up electrons. As a result, the photons were able to move easily through space.

9.) When the Cosmic Microwave Background light was made, its wavelength was:
a.) about 1 nanometer (10-9 meters)
b.) about 10 nanometers (10-8 meters)
c.) about 100 nanometers (10-7 meters)
d.) about 1 micron (10-6 meters)
e.) about 10 microns (10-5 meters)
f.) about 100 microns (10-4 meters)
g.) about 1 millimeter (10-3 meters)
Answer: "c", the answer, 100 nanometers, is much shorter than the current wavelength because the Universe (and so the photons in it) has stretched by a factor of 1100 (in all directions) since the Cosmic Microwave Background light was made.

10.) What is the Cosmic Microwave Background? (your answer should state what the CMB is made of, how it was made, and how it has been tranformed over the years since it was made.)
Answer: What is it: The Cosmic Microwave Background (CMB) is sea of microwave photons that move through the Universe now.
How was it made: When the Universe was young, it was filled with more energetic photons. After pair production ceased, the photons found it hard to efficiently move far because they bounced off of charged particles. That is until the electrons & protons (and electrons & helium nuclei) combined to make neutral atoms (Universe's age then = 380,000 years, end of Era of Nuclei). Then, the photons didn't have nearly as much trouble sailing through space. Most of these photons still exist today and simply sail through the Universe. Combined, they compose the CMB.
How has it been transformed: When these photons were made, they had much shorter wavelengths. Their wavelengths increased as the space in which they existed stretched.

11.) The Cosmic Microwave Background has slight variations in its wavelengths. The shorter photons come from regions of the early Universe that were a little warmer than the other parts. The angular size of these regions is about 1 degree. What caused this variation in the material in the early Universe?
a.) quantum fluctuations in the material of the Universe at earlier times
b.) the decay of neutrons into protons
c.) the production of matter and antimatter d.) the annihilation of matter and antimatter

12.) In the time since the Cosmic Microwave Background was emitted, what happened to the regions that emitted the slightly more energetic photons ?
a.) They were regions that contained antimatter, so they annihilated with surrounding regions that had matter
b.) They were hotter than surrounding matter, so expanded, creating the voids we see now in the Universe
c.) They were denser than the surrounding regions, dense enough to gravitationally collapse, resulting in clusters of galaxies
d.) They mixed with the neighboring region, resulting in an even distribution of matter throughout space
Answer: "c" they were denser, so spawned clusters of galaxies

13.) The observed characteristics of the Cosmic Microwave background are the same as expected from models of the universe. But if there had been much more mass density in the Universe at the time when the Cosmic Microwave Background photons were "set free", so much more density that it would warp spacetime, how would we know? (i.e. what would be different about the Cosmic Microwave Background?)
a.) The size of the hot-spots in the Cosmic Microwave Background would look larger
b.) The temperature calculated from of the Cosmic Microwave Background would be higher
c.) The intensity of the Cosmic Microwave Background would be greater
Answer: "a" the hot-spots in the Cosmic Microwave Background would have larger angular sizes than the approximately 1 degree size that we see

We haven't covered the exciting things that happen to forces in the Planck, GUT, and Electroweak Era's, so I am treading lightly on them (for now).
14.) In 1 sentence, what is the GUT force?
Answer: the GUT force is the force that is a combination of the strong force, weak force, and electromagnetic force. It is just as valid to say that the GUT force is the combination of the strong force and the electroweak force. (By the way, GUT stands for Grand Unified Theory.)

15.) Inflation was caused by:
a.) Pair production
b.) The creation of antimatter
c.) The splitting up of the GUT force
d.) The decay of neutrons into protons and subatomic particles
Answer: "c" the splitting of the GUT force into electroweak force & the strong force