A parametrization of the growth index of matter perturbations in various Dark Energy models and observational prospects using a Euclid-like survey

Understand

We provide exact solutions to the cosmological matter perturbation equation in a homogeneous FLRW universe with a vacuum energy that can be parametrized by a constant equation of state parameter $w$ and a very accurate approximation for the Ansatz $w(a)=w_0+w_a(1-a)$.

• We compute the growth index $\gamma=\log f(a)/\log\Om_m(a)$, and its redshift dependence, using the exact and approximate solutions in terms of Legendre polynomials and show that it can be parametrized as $\gamma(a)=\gamma_0+\gamma_a(1-a)$ in most cases.
• We then compare four different types of dark energy (DE) models: $w\Lambda$CDM, DGP, $f(R)$ and a LTB-large-void model, which have very different behaviors at $z\gsim1$.
• 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 $z\simeq 2$.