Contiguous redshift parameterizations of the growth index

Understand

The growth rate of matter perturbations can be used to distinguish between different gravity theories and to distinguish between dark energy and modified gravity at cosmological scales as an explanation to the observed cosmic acceleration.

• We suggest here parameterizations of the growth index as functions of the redshift.
• The first one is given by $\gamma(a)=\tilde\gamma(a) \frac{1}{1+(a_{_{ttc}}/a)}+\gamma_{_{early}} \frac{1}{1+(a/a_{_{ttc}})}$ that interpolates between a low/intermediate redshift parameterization $\tilde\gamma(a)=\gamma_{_{late}}(a)= \gamma_0 + (1-a) \gamma_a$ and a high redshift $\gamma_{_{early}}$ constant value.
• For example, our interpolated form $\gamma(a)$ can be used when including the CMB to the rest of the data while the form $\gamma_{_{late}}(a)$ can be used otherwise.