ASTR508

Cosmology

Problem Set #1

The Isotropic Universe

Professor: Julio F. Navarro

Spring 2016

Note: This problem set is an assignment and should be returned to me for grading by Feb 11. Each problem is worth 1 point except for #7, which is worth 2 points.

  1. Use the equivalence principle to estimate the gravitational redshift incurred by a light source suspended at height h in a uniform gravitational field of acceleration g.
  2. For what spectral energy distribution does the K-correction (expressed in magnitude units) vanish?
  3. Derive the redshift dependence of a galaxy's (monochromatic and bolometric) surface brightness. Do they depend only on redshift or also on the dynamical history of the universe? Interpret.
  4. What limits may be derived on the cosmological constant from the fact that QSO's with z=5 have been observed?
  5. Can the age of the universe be longer than H0-1 in a flat (k=0) universe? If so, derive the conditions under which this happens.
  6. Imagine that you live in a closed matter-dominated "dust" universe. Does the particle horizon ever get to be as large as the whole universe? If so, when is the first time that this happens?
  7. Assume again that you live in a flat, matter-dominated "dust" universe. Derive the particle horizon scale at recombination (z=1000). What angle does this subtend for an observer at z=0?
  8. In the same universe as the previous question, compute, as a function of cosmic time, the "proper" and "comoving" distance  between a photon emitted at t=0 and an observer who receives it at the present time. Plot "proper" distance in units of the horizon scale at z=0 and interpret.
  9. Again in this universe, at what redshift is the angular diameter of a "standard rod" minimum?