We investigate the cosmic evolution of the linear bias in the framework of a flat Friedmann-Lemaître-Robertson-Walker spacetime. We consider metric perturbations in the Newtonian gauge, including Hubble scale effects. Making the following assumptions, (i) scale-independent current epoch bias b0, (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 general relativity 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 γ and the observable value of the tracer power spectrum normalization σ8(z). We show how this connection can be used as an observational test of general relativity on extragalactic scales.