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

Testing General Relativity Using the Evolution of Linear Bias