General questions (should be answered at some length, about 2 pages):
  1. Describe the visible matter content in the Universe: stars, galaxies, clusters, itersellar medium, etc. Give typical masses, sizes, distances, luminosities, desities, ages.
  2. Describe the dark matter problem in the galactic context.
  3. What is the observational basis for assuming that the Universe is homogenous and isotropic?
  4. Describe the observational evidence for the expanssion of the Universe.
  5. Describe the observational evidence for the hot big bang.
  6. Why classical physics is not adequate in describing the big bang?
  7. Describe in general terms the evolution of the Universe from the big bang to the present epoch.
  8. Describe the horizon and flatness problems and their inflationary solution.
  9. Describe the cosmic nucleosynthesis of elements. Which elements could not be produced by the big bang Universe? Why? Where and how they have been produced?
  10. Describe how the background microwave radiation probes the physics of early Universe.
Computational questions:
  1. A spherical body of a perfect gas in equilibrium has radius R and mass M. Estimate the central pressure. Apply to the Sun.
  2. Derive two equations that govern expanssion of the Universe. Use Newton's theory.
  3. Show that in the radiation dominated universe the scale factor grows as the square root of time, and density falls down as the fourth power of the scale factor. Why this is relevant for the argument of the hot big bang?
  4. Estimate the value of the redshift at the recombination epoch.
  5. Estimate the value of redshift when the matter and radiation desities were comparable.
  6. Calculate the size of the horizon at the last scattering surface (no inflation).
  7. Assume the flat Universe with the Hubble constant H_0 = 70km/sec/Mpc. What is the current proper distance to a galaxy with z = 7 in: (a) matter dominated Universe, (b) radiation dominated Universe, (c) lambda dominated Universe?
  8. Derive the Jean's criterion.
  9. Estimate the dark matter density in our Galaxy near the Sun location from the fact that the rotational curve is flat there.
  10. Calculate the rate of matter creation in the hypothetical steady state Universe.