  Measurements of the growth index $\gamma(z)$ provide a clue as to whether
Einstein's field equations encompass gravity also on large cosmic scales, those
where the expansion of the universe accelerates. We show that the information
encoded in this function can be satisfactorily parameterized using a small set
of coefficients $\gamma_i$ in such a way that the true scaling of the growth
index is recovered to better than $1\%$ in most dark energy and dark gravity
models. We find that the likelihood of current data is maximal for
$\gamma_0=0.74\pm 0.44$ and $\gamma_1=0.01\pm0.46$, a measurement compatible
with the $\Lambda$CDM predictions. Moreover data favor models predicting
slightly less growth of structures than the Planck LambdaCDM scenario. The main
aim of the paper is to provide a prescription for routinely calculating, in an
analytic way, the amplitude of the growth indices $\gamma_i$ in relevant
cosmological scenarios, and to show that these parameters naturally define a
space where predictions of alternative theories of gravity can be compared
against growth data in a manner which is independent from the expansion history
of the cosmological background. As the standard $\Omega$-plane provides a tool
to identify different expansion histories $H(t)$ and their relation to various
cosmological models, the $\gamma$-plane can thus be used to locate different
growth rate histories $f(t)$ and their relation to alternatives model of
gravity. As a result, we find that the Dvali-Gabadadze-Porrati gravity model is
rejected with a $95\%$ confidence level. By simulating future data sets, such
as those that a Euclid-like mission will provide, we also show how to tell
apart LambdaCDM predictions from those of more extreme possibilities, such as
smooth dark energy models, clustering quintessence or parameterized
post-Friedmann cosmological models.
