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.
- 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.
- For what spectral energy distribution does the
K-correction (expressed in magnitude units) vanish?
- 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.
- What limits may be derived on the cosmological
constant from the fact that QSO's with z=5 have
been observed?
- 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.
- 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?
- 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?
- 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.
- Again in this universe, at what redshift is the angular diameter of a "standard
rod" minimum?