Homework 5 : Cosmological models and the CMB

(due at the start of class on the 7^th November 2002)

1. [5 points] State the Cosmological Principles. Briefly explain why we are forced to make these assumptions. What is the observational evidence that supports these assumptions?

2. Suppose that we discover a quasar with a redshift of z=7.
1. [3 points]What is the scale factor R of the Universe at the time that this quasar existed relative to the present scale factor?
2. [3 points] If we assume that galaxies have not been created or destroyed, how much closer together will galaxies be (on average) at the time that this quasar existed compared with the present time?
3. [4 points] Suppose that the quasar undergoes a flare that lasts for 1 day as seen by an observer sitting nearby to the quasar. How long will we observe the flare to last?

3. [5 points] Define the particle horizon. To what extent can the distance to the particle horizon be considered to describe the size of the Universe?

4. [5 points] Today, the cosmic microwave background (CMB) has a characteristic wavelength of l=5cm. When we look out into the Universe, at what redshift would we have to look to find a time and place where the CMB has a wavelength of l=1cm. By what factor would the “scale factor” of the Universe be smaller at a time when the CMB has l=1cm.

5. [5 points extra credit] Suppose that the Universe were not homogeneous, i.e., different parts of the Universe had different average properties. Explain why this would effect the concept of “cosmic time”.