  Assuming a simple form for the growth index gamma(z) depending on two
parameters gamma_0 = gamma(z=0) and gamma_1 = gamma'(z=0), we show that these
parameters can be constrained using background expansion data. We explore
systematically the preferred region in this parameter space. Inside General
Relativity we obtain that models with a quasi-static growth index and gamma_1 =
-0.02 are favoured. We find further the lower bounds gamma_0 > 0.53 and gamma_1
> -0.15 for models inside GR. Models outside GR having the same background
expansion as LCDM and arbitrary gamma(z) with gamma_0 = gamma_0^{LCDM}, satisfy
G_{eff,0}>G for gamma_1 > gamma_1^{LCDM}, and G_{eff,0}<G for gamma_1 <
gamma_1^{LCDM}. The first models will cross downwards the value G_{eff}=G on
very low redshifts z<0.3, while the second models will cross upwards G_{eff}=G
in the same redshift range. This makes the realization of such modified gravity
models even more problematic.
