Review Questions

1. What is the interpretation of cosmological redshift? What is the quantified relationship between redshift and the expansion factor?  

2. If the redshift of a photon is measured to be z = 1, by what factor was the universe smaller when the photon was emitted?  What if the photon has a redshift z = 2? What if the photon has a redshift z = 3?  [see the pattern?]

3. Write down the functions E(t) and E'(t) in terms of redshift, i.e., E(z) and E'(z).  In the 737 Cosmology. at approximately what redshift did the expansion of the Universe change from deceleration to acceleration?

4. What is lookback time?  In the 737 Cosmology, at what approximate redshift did the lookback time equal the age of the universe, i.e., when the Universe was half its age?

5. What is the Hubble distance and what is its magnitude? Write down its mathematical expression. 

6. In your own words, define the (i) radial co-moving distance, (ii) radial proper distance, (iii) transverse co-moving distance, and (v) transverse proper separation. 

7. In your own words, what is (i) the angular diameter distance, (ii) the luminosity distance, and (iii) the absorption distance?

8. At redshift z = 10, two galaxies have a co-moving separation of 1 Mpc.  What is their proper separation at z = 0?  Two galaxies have a proper separation of 100 kpc at z = 0.  What is their co-moving separation at z= 2?  At z = 5? Explain your answers.

9. Let's revisit the transverse co-moving distance.  Explain how it is related to the radial co-moving distance and the curvature of the Universe.  In a flat Universe, what is the exact relationship between the transverse co-moving distance and the radial co-moving distance? 

10. Explain why the angular diameter distance at first increases with redshift, peaks around z = 1.4, and then decreases toward higher redshifts.

11. Explain why the luminosity distance is (1+z)2 times the angular diameter distance? In other words, where does each factor of 1+z derive from?

12. In your own words, state the definition of the redshift path density, dN/dz? For a non-evolving population of absorbers ("fixed targets"), this function increases with redshift according to (1+z)2/E(z). In an expanding spacetime, what is this functional form accounting for in terms of fixed targets intercepted by a pencil beam sightline?

13. Describe the fundamental difference between the recessional velocity and the peculiar velocity.  

14. For peculiar velocities, what is the approximate velocity difference between two z ~ 0 galaxies that are separated by ∆z =0.0001, 0.001, 0.01, and 0.1?  What are the peculiar velocity differences if they are roughly at z ~ 1?  At what ∆z does one need to account for relativistic corrections to compute accurate peculiar velocity differences?

15. Why is the relativistic velocity formula of Special Relativity not applicable for computing cosmic recessional velocities? Can recessional velocity ever be directly measured, or is its computed value totally dependent on the cosmological model?

16. Considering Equation 25.100 and Figure 25.17, at what redshift does the recessional velocity exceed the speed of light? What is the recessional velocity of a galaxy at z = 4? Does this answer surprise you? Why or why not? 

Problems

1. Under construction