Relationship between photometric colour and redshift In this paper, the authors describe the theoretical relationship between photometric colours, particularly in Figures 1 and 6:




Since the colour is the difference between two magnitudes, and the redshift is defined as
$z=\frac{\lambda'-\lambda_0}{\lambda_0}$

I would have thought that the colour-z relationships would simply be a downward curve, since the light gets redshifted (goes down in frequency), and the ratio of two magnitudes is constant with redshift.

Why do the colour-z relationships in this paper (and in others I've seen) show such a complex relationship?
The main reason is that the intrinsic spectra of galaxies are complex and therefore a redshift of their spectrum, whilst leading to a redder spectrum overall, does not necessarily lead to reddening in all colours.

For instance if there is apeak in the intrinsic spectrum, then as that peak moves redward, then colours formed from bands on the same side or straddling the peak in wavelength would behave differently.

The dramatic redward turn up at high redshifts (note, a large colour is redder) is caused by the "Lyman break" moving through the colour bands. Basically, the intrinsic spectrum is self-absorbed at wavelengths shortward of 91.2 nm by neutral hydrogen. This absorption edge is redshifts into the visible region at redshifts bigger than 3, causing the bluer bands to essentially disappear and any colour formed with them to become very red.