While reading about the discovery of quasars and the spectroscopic analysis of 3C 273 in this paper by Maarten Schmidt, I came across the following quote:
At these distances, corrections to luminosities depend on the specific world model. For an approximate determination of the fluxes in the emission lines we use the formulae given by Sandage (1961) based on Mattig (1958). For the energy contained within an emission line, in which we integrate over the entire profile, the correction to the inverse square law is of the form $(1 + z/2)^2$ if the cosmological constant and deceleration parameter are zero. It is $(1 + z)^2$ for the steady-state model.
First, why is a correction to the inverse square law necessary? Is it to do with interstellar extinction?
Second, why are the two models different? I understand what the cosmological constant and deceleration parameter are, but why is the redshift prediction for a steady state model twice as much as when $\Lambda=q=0$?