  We investigate the cosmic evolution of the linear bias in the framework of a
flat FLRW spacetime. We consider metric perturbations in the Newtonian gauge,
including Hubble scale effects. Making the following assumptions, (i) scale
independent current epoch bias $b_0$, (ii) equal accelerations between tracers
and matter, (iii) unimportant halo merging effects (which is quite accurate for
$z<3$), we analytically derive the scale dependent bias evolution. The
identified scale dependence is only due to Hubble scale evolution GR effects,
while other scale dependence contributions are ignored. We find that up to
galaxy cluster scales the fluctuations of the metric do not introduce a
significant scale dependence in the linear bias. Our bias evolution model is
then used to derive a connection between the matter growth index $\gamma$ and
the observable value of the tracer power spectrum normalization $\sigma_8(z)$.
We show how this connection can be used as an observational test of General
Relativity on extragalactic scales.
