Please answer the following (you will need to refer to the attachment for some of the questions):
a) Describe what is meant by redshift and how spectroscopic observations of extragalactic objects may be used to deduce their redshifts.
b) What is meant by the term metric? The Friedmann-Robertson-Walker metric for a homogeneous and isotropic universe is given by the function in the attached document (please view the attachment)
c) What does the above expression become in the case of a light-ray? Hence derive an integral expression for a light-ray which leaves the origin at time t_em and reaches a co-moving distance r_0 at time t_obs. A second ray is emitted a time dt after the first. By considering the two intervals as corresponding to successive wave crests, derive the relation (please view the attachment)
d) How does the separation of galaxies today compare with the separation of galaxies when light left the galaxies we observe at redshift 1.
This solutions contains explanations on red-shift, metrics, light-rays and galaxies in the context of astrophysics.