Download Solutions to HW 1-2

Physics 120 Reading Homework Assignment #1-2 Name:_____________________
Due: Sunday 10 PM, January 29, 2017
(This is a double assignment covering the first two weeks of class.)
Please insert your name where indicated in the upper right-hand corner of this page. Expected
length of answers is approximately one paragraph for each question. Please expand this word-file
and insert your answers in-place below.
Feel free to discuss questions and concepts with other students from the class. This is
encouraged. However, when you sit down to answer the questions in the homework assignment,
you must submit your own answers. Please copy this word file and enter your responses below
each question. Be concise but complete.
Your completed homework assignments must be uploaded on Canvas by the specified due date
and time in order to receive credit.
1) What role does matter have in determining the evolution and the possible fate of the
Universe? Describe the evolution of the Universe implied by each of the curves in the graph
labeled “Expansion of the Universe” on page 3 of the WMAP reading.
Matter plays a central role in determining the evolution of the Universe, particularly its
density. The greater the density, the greater is the gravitational pull that all the matter
exerts on itself, slowing down the expansion rate. A critical density is reached (green curve)
if the gravitational pull is enough to continually slow down the expansion rate, but not
enough to ever stop the expansion; if the density is higher than the critical value the
Universe will eventually stop expanding and will start shrinking into a “Big Crunch”
(yellow curve); if the density is lower than the critical one the expansion rate may
continually slow down, but less so than it does at critical density (blue curve); if the density
is even lower the expansion will keep accelerating (red curve).
2) Give three experimental “tests” of the Big Bang Model and state in a sentence or two
each their results that support the model.
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Edwin Hubble observation (1929) that galaxies are receding from us at a speed
proportional to their distance, is in agreement with a universal expansion where all
galaxies are receding from each other. If we “run the movie backward” we would
see the Universe shrinking into a very small primordial state at which time the Big
Bang happened.
Big Bang models of the primordial nucleosynthesis can predict the relative fractions
of light nuclei in ordinary matter; particularly the fraction of helium turns out to be
insensitive to the total abundance of ordinary matter in the Universe, above a
certain threshold; its relative abundance of 24%, as measured from various
observations, is in striking agreement with predictions from the Big Bang
nucleosynthesis.
The Cosmic Microwave Radiation (CMB), first observed in 1965 and later studied
in great detail over more than four decades, matches expectations of a primordial
light emitted by the hot early Universe, few hundred thousands years after the Big
Bang, when atoms were formed and the Universe became transparent to
electromagnetic radiation.
3-4) Explain what it means when we say “the farther away we can see, the farther back in
time we view.” As we “look backward in time” we discover that the Universe was hotter
earlier to the extent that particle creation occurred. How can more massive particles be
created more easily when it is hotter? What are some general constraints on the masses and
types of particles that can be created at a given time for a given energy (e.g. based on
conservation laws)?
Since light travels at a finite speed, we see far away objects as they appeared back when
their light was emitted. For example, the light emitted by the Sun takes about 8 minutes to
reach us; the farthest objects observed by astronomers are some billion light-years away,
which means that we see them as they were billions of years ago!
As we go back in time the Universe was much denser and hotter. Higher temperatures
means that on average particles had a higher kinetic energy; when they collide their kinetic
energy can be converted into mass according to Einstein’s equation: E = mc2, where c is the
velocity of light. Since the velocity of light is very large, a large amount of energy is needed
to produce mass. In addition to conservation of mass-energy, these processes have to obey
other conservation laws. Some of these are:
 electric charge (equal number of positively and negatively charged particles must be
produced)
 matter/antimatter (equal number of particles and antiparticles for each particle
type)
5) Name two problems with the Big Bang Theory (not the TV show!) that are resolved by
inflation, and how inflation purports to resolve them.
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Flatness problem: in the Big Bang theory the curvature of the Universe grows with
time and a flat Universe would be quite unlikely, requiring a “fine tuning” of its free
parameters. Inflation solves this problem because during the rapid exponential
expansion, any initial curvature of the Universe would be stretched to near flatness.
Horizon problem: the CMB is strikingly uniform in every direction we look in the
sky. Opposite directions of the sky are too far away to have ever been in casual
contact in order to come to thermal equilibrium (i.e. to communicate to each other
the “information” about their temperature – remember nothing can travel faster
than light!). Inflation solves this problem by assuming that these different parts of
the Universe were in thermal equilibrium some time after the Big Bang and then got
separated later during the rapid expansion.
Monopole problem: the Big Bang theory predicts the existence of a large amount of
magnetic monopoles, which have never been observed. These monopoles may have
been dispersed over very large distances during inflation, reducing their abundance
in the Universe to an extent that they are not detectable by our current experiments.
Structure formation: inflation may also explain the formation of structures in the
Universe, as a consequence of the sudden “amplification” over galactic scales of
small quantum fluctuations present in the small Universe before inflation.
To be complete, Trefil in subsequent reading also mentions the anti-matter problem
although for the above question inflation does not seems to help resolve this
dilemma. It is possible that there is some process that we haven't discovered yet that
creates more matter than antimatter. It is also possible that there was more matter
than antimatter created at the time of the Big Bang, but this cannot be justified in
any theoretical approaches.
(You only needed to mention two of the above)
6-7) a) Describe how quantum mechanics is necessary for inflation to have occurred in the
early Universe.
b) Explain the origin of this rapid expansion (i.e. inflation) of the Universe.
c) What propelled the expansion (i.e. forces, energy or something else)?
d) What is the primary advantage of the “new inflationary scenario” over the standard
inflationary scenario according to Trefil?
a) Quantum mechanics is necessary to explain one of the most plausible mechanisms that
led to inflation, using the concepts of “false vacuum” and “tunneling”.
b) In these inflationary models, at the beginning the entire Universe was in a “false
vacuum” state, a state which corresponds to a local minimum of the potential of an
“inflaton” field (which Trefil identifies with the Higgs field) that permeated the early
Universe. According to the laws of quantum mechanics, if the potential barrier of the local
minimum is not infinite there is a small but finite probability that the state can be found
across the potential barrier. We say that the state “tunneled” through the potential barrier,
towards a lower potential state.
c) After tunneling, the state “rolls” down the potential going towards the minimum; by
doing so, it reduces its potential energy that is then released in the form of kinetic energy
and mass.
d) In the “new inflationary scenario” the Universe freezes in a single domain in a much
“smoother” process which reduces the number of expected magnetic monopoles, which
have not been observed so far.
8-9) The GUT era must have been fascinating.
a) Please give the time‐span that Trefil associates with this era, the forces and particles that
were expected to be active at that time.
b) Which force “freezes” at the end of this era (please give the forces before and after this
freezing)?
a) The GUT era corresponds to the time that goes from the Planck time 10-43 to about 10-35
after the Big Bang. During this time only two forces existed: the gravitational force and a
second force which is the “unification” of the current strong, weak and electromagnetic
forces. These forces would be unified in the sense that they would be described by a single
theory and have the same strength. The GUT era was dominated by the presence of the Xbosons, the particles that carry the unified strong-weak-electromagnetic force. Leptons and
quarks could turn into each other by exchanging X-bosons.
b) The strong force freezes at the end of the GUT era. Before the freezing only two
forces existed: the gravitational force and the strong-weak-electromagnetic force.
After the freezing there were three forces: the gravitational force, the strong force
and the electro-weak force.
10) a) Which topics did you find particularly complicated and had difficulty
understanding? What specific questions do you have about this (these) topic(s)?
b) Which topics did you find particularly interesting and would like to discuss further in
class? Any specifics or questions that you wish to add on each topic?
Any answers to these questions receives credit.