Is the CMB shift parameter connected with the growth of cosmological perturbations?

We verify numerically that in the context of general relativity (GR), flat models which have the same Omega(m) and cosmic microwave background (CMB) shift parameter R but different H(a) and w(a) also have very similar (within less than 8 per cent) growth of perturbations even though the dark energy density evolution is quite different. This provides a direct connection between geometrical and dynamical tests of dark energy and may be used as a cosmological test of GR.