Box: Relativistic Doppler effect

The relativistic expansion velocity is a fraction ν_exp of the speed of light, we have

${\nu }_{exp}=B\sqrt{L}.$ (B1)

The increasing velocity causes a prolongation of the wavelength, the Doppler effect. The relativistic velocity difference is obtained from, cf. HyperPhysics/Relativistic Doppler,

${\nu }_{\text{Δ}}=\frac{{\nu }_{exp0}+{\nu }_{exfl}}{1+{\nu }_{exp0}{\nu }_{exfl}}.$ (B2)

The scale factor a_fl is obtained from

$a_{fl}=\sqrt{\frac{1-{\nu }_{\text{Δ}}}{1+{\nu }_{\text{Δ}}}}.$ (B3)

The value obtained by iteration is a_fl = 0.0173, the same as in Figure 4.