Homework Assignment #6
This assignment is due at the beginning of class on Friday, October 24. Late homework will not be accepted, including homework turned in at the end of class. If you can't make it to the beginning of class, make sure to turn your homework in to me beforehand.
You must do the first three problems. Each of those problems will be worth 10 points. If you make a sincere, honest effort to answer each question, you will receive at least 5 points of credit.
Staple your homework! If you require more than one page to complete the homework, fasten the multiple pages together with a staple; folding the corner won't cut it. If your homework has multiple pages but you fail to staple, you will be docked 3 points.
The last two problems are given to you as additional review problems. You do not need to turn them in, and they will not be graded when you do. However, solutions to them will be posted along with the solutions to the first three problems. You may want to do them if you think you need extra review in the class.
Please write out the problem statement at the top of your solution. (This is for two reasons; it is so I can know which problem you answered, and that you answered the right problem from the book. It also will make your graded homework more useful as a study aid later.)
In class, we discussed that about 2/3 of the energy density of the Universe is in dark energy. What makes up most of the energy density of our Galaxy? How do you know? Is this at odds with dark energy making up most of the energy density of the Universe? Why or why not?
When we look to distant redshifts, we sometimes say we are looking back to the "era of deceleration". Suppose that dark energy acts like Einstein's cosmological constant, i.e. its density is constant and does not change as the Universe expands. If the Universe's expansion is accelerating now, why would we say that the expansion is decelerating for galaxies with very high redshifts?
A typical Cosmic Microwave Background (CMB) photon observed today has a wavelength of 1 mm (=10-3 m). The CMB was emitted more than 13 billion years ago, when the Universe was about 1/1100th its current size. What was the wavelength of a typical CMB photon when it was emitted? Is this in the visible range of the electromagnetic spectrum? If so, what color would it be? If not, in what range of the electromagnetic spectrum is it?
(The problems below will not be graded, and need not be turned in.)
Recall your results on last week's homework for the age of the Universe assuming that the expansion rate hadn't changed. In the absense of dark energy, the Universe's expansion rate would have been slowing down since the big bang. Before the discovery of dark energy, there was a cosmological age crisis, in that the oldest stars in (found in globular clusters around our Galaxy) are known to be about 13 billion years old, whereas many cosmologists thought the Universe had a mass density equal to the critical density and was less aged! Without dark energy, and given a current expansion rate, would you need a Universe that is very low density or very high density to accomidate these old globular clusters? Why? Would cosmologists led to conclude this value of the mass density believe that the Universe would recollapse in a Big Crunch, or expand forever into a Big Chill?
Nucleosynthesis in the Big Bang created only Hydrogen, Helium, and a little Lithium, and almost nothing else. However, observations of interstellar gas clouds show a measurable concentration of Carbon, Oxygen, Iron, and other elements. What can you conclude about the gas in these interstellar clouds? (You may not know the answer to this question, but you should recognize at least that there is a problem! In a couple of weeks, we will have discussed everything you need to know to understand the answer to this question.)