Growth Diagnostics for Dark Energy models and EUCLID forecast
  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.
