Measurements of the growth index of linear matter density fluctuations \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 , given this formalism and the \Lambda Cold Dark Matter ( \Lambda CDM ) expansion model of Planck , is maximal for \gamma _ { 0 } = 0.74 ^ { +0.44 } _ { -0.41 } and \gamma _ { 1 } = 0.01 ^ { +0.46 } _ { -0.46 } , a measurement compatible with the \Lambda CDM predictions ( \gamma _ { 0 } = 0.545 , \gamma _ { 1 } = -0.007 ) .
In addition , data tend to favor models predicting slightly less growth of structures than the Planck \Lambda CDM 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 \Lambda CDM predictions from those of more extreme possibilities , such as smooth dark energy models , clustering quintessence or parameterized post-Friedmann cosmological models .