General Astronomy - Spring
2011
Homework #11 - due April 25
1. (3 pt) When was the energy density of the
universe dominated by matter, radiation, and dark energy?
2. (4 pt) Using Newtonian mechanics, derive
an equation for the critical density of the Universe given a Hubble
constant H0.
3. (4 pt) Show that the scale factor, a,
of
the universe at a given time in the past is related to the redshift,
z, that we now observe for
light emitted by objects at that time as z = 1/a-1, where we define a=1 at the current time (in the
notation of the book a(t0) = 1).
4. (4 pt) How does the energy density of radiation vary with the scale
factor a? The current
energy density in radiation is 0.260 MeV m-3. What was
the energy density at the time of recombination (z = 1100).
5. (5 pt) Starting from the Lemaitre equation in the form on slide 12
of lecture 17, show that a universe dominated by the cosmological
constant energy density will expand at an exponential rate. Hint:
guess a solution and show that it satisfies the equation.