Deriving Hubble redshift in closed Universe from Maxwell equations

1. The problem statement, all variables and given/known data
I should derive the Hubble law redshift from Maxwell equations in closed Universe.
2. Relevant equations
The metric of closed Universe is [tex]ds^2 = dt^2 - a^2(t)\left(d\chi^2 + \sin^2 \chi d\theta^2 + \sin^2 \chi \sin^2 \theta d\phi^2\right)[/tex].
The Hubble law redshift: [tex]\frac {\lambda(t)} {\lambda(t_0)} = \frac {a(t)} {a(t_0)}[/tex].
The wave equation for 4-potential is
[tex]\nabla_\mu F^{\mu\nu} = 0 \Rightarrow \partial_\mu \left(\sqrt{-g}g^{\mu\rho}g^{\nu\sigma}\left(\partial_\rho A _\sigma - \partial_\sigma A_\rho\right)\right)[/tex]
3. The attempt at a solution
As you can see the wave equation is very difficult to solve. Is there another way to show the Hubble redshift low for electormagnetic waves using Maxwell equations?

 

I guess I've found the solution in this paper: http://prd.aps.org/abstract/PRD/v8/i12/p4297_1