Parametrizations of the growth index and EUCLID-like survey forecasts
Bueno Belloso, Alicia (Instituto de Física Teórica (UAM/CSIC))

We provide exact solutions to the cosmological matter perturbation equation in a homogeneous FLRW universe with a vacuum energy that can be parametrized with a variable equation of state parameter w(a) = w0 + wa(1 − a). We compute the growth index γ = logf(a)/logΩm(a), and its redshift dependence, using the exact solutions in terms of Legendre polynomials and show that it can be parametrized as γ(a) = γ0 + γa(1 − a). We then compare four different types of dark energy (DE) models: wΛCDM, DGP, f(R) and a LTB-large-void model, which have very different behaviors at z ∼> 1. This allows us to study the possibility to differentiate between different DE alternatives using wide and deep surveys like EUCLID, which will measure both photometric and spectroscopic redshifts for several hundreds of millions of galaxies up to redshift z ≃ 2. We do a Fisher matrix analysis for the prospects of differentiating among the different DE models in terms of the growth index, taken as a given function of redshift or with a principal component analysis, with a value for each redshift bin. We use as observables the complete and marginalized power spectrum of galaxies P(k) and the Weak Lensing (WL) power spectrum. We find that, using P(k), one can reach (2%, 5%) errors in (w0,wa), and (4%, 12%) errors in (γ0,γa), while using WL we get errors at least twice as large. These estimates allow us to differentiate easily between DGP, f(R) models and ΛCDM, while it would be more difficult to distinguish the latter from a variable equation of state parameter or LTB models using only the growth index.