GCG Parametrization for Growth Function and Current Constraints

We study the linear growth function $f$ for large scale structures in a cosmological scenario where Generalised Chaplygin Gas (GCG) serves as dark energy candidate. We parametrize the growth index parameter as a function of redshift and do a comparative study between the theoretical growth rate and the proposed parametrization. Moreover, we demonstrate that growth rates for a wide range of dark energy models can be modeled accurately by our proposed parametrization. Finally, we compile a data set consisting of 28 data points within redshift range (0.15,3.8) to constrain the growth rate. It includes direct growth data from various projects/surveys including the latest data from the Wiggle-Z measurements. It also includes data constraining growth indirectly through the rms mass fluctuation $σ_8(z)$ inferred from Ly-$α$ measurements at various redshifts. By fitting our proposed parametrization for $f$ to these data, we show that growth history of large scale structures of the universe although allows a transient acceleration, one cannot distinguish it at present with an eternally accelerating universe.

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