Growth Diagnostics for Dark Energy models and EUCLID forecast

TL;DR

This paper introduces new parameters based on matter perturbation growth to distinguish dark energy models, demonstrating their effectiveness with EUCLID forecast data and highlighting differences from the standard b2CDM model.

Contribution

The paper proposes a novel set of parameters $(r_{g}, s_{g})$ for analyzing dark energy models using growth of matter perturbations, offering a new diagnostic tool.

Findings

$(r_{g}, s_{g})$ are exactly (1,1) for b2CDM at all redshifts

Different dark energy models follow distinct trajectories in the $(r_{g}, s_{g})$ phase plane

Future EUCLID measurements can tightly constrain these parameters, ruling out some models.

Abstract

In this work we introduce a new set of parameters $(r_{g}, s_{g})$ involving the linear growth of matter perturbation that can distinguish and constrain different dark energy models very efficiently. Interestingly, for $\Lambda$CDM model these parameters take exact value $(1,1)$ at all red shifts whereas for models different from $\Lambda$CDM, they follow different trajectories in the $(r_{g}, s_{g})$ phase plane. By considering the parametrization for the dark energy equation of state ($w$) and for the linear growth rate ($f_{g}$), we show that different dark energy behaviours with similar evolution of the linear density contrast, can produce distinguishable trajectories in the $(r_{g}, s_{g})$ phase plane. Moreover, one can put stringent constraint on these phase plane using future measurements like EUCLID ruling out some of the dark energy behaviours.