Contiguous redshift parameterizations of the growth index
  The growth rate of matter perturbations can be used to distinguish between
different gravity theories and to distinguish between dark energy and modified
gravity at cosmological scales as an explanation to the observed cosmic
acceleration. We suggest here parameterizations of the growth index as
functions of the redshift. The first one is given by $\gamma(a)=\tilde\gamma(a)
\frac{1}{1+(a_{_{ttc}}/a)}+\gamma_{_{early}} \frac{1}{1+(a/a_{_{ttc}})}$ that
interpolates between a low/intermediate redshift parameterization
$\tilde\gamma(a)=\gamma_{_{late}}(a)= \gamma_0 + (1-a) \gamma_a$ and a high
redshift $\gamma_{_{early}}$ constant value. For example, our interpolated form
$\gamma(a)$ can be used when including the CMB to the rest of the data while
the form $\gamma_{_{late}}(a)$ can be used otherwise. It is found that the
parameterizations proposed achieve a fit that is better than 0.004% for the
growth rate in a $\Lambda$CDM model, better than 0.014% for
Quintessence-Cold-Dark-Matter (QCDM) models, and better than 0.04% for the flat
Dvali-Gabadadze-Porrati (DGP) model (with $\Omega_m^0=0.27$) for the entire
redshift range up to $z_{_{CMB}}$. We find that the growth index parameters
$(\gamma_0,\gamma_a)$ take distinctive values for dark energy models and
modified gravity models, e.g. $(0.5655,-0.02718)$ for the $\Lambda$CDM model
and $(0.6418,0.06261)$ for the flat DGP model. This provides a means for future
observational data to distinguish between the models.
