Versatile parametrization of the perturbation growth rate on the phantom brane

Abstract: We derive an analytical expression for the growth rate of matter density perturbations on the phantom brane (which is the normal branch of the Dvali-Gabadadze-Porrati model). This model is characterized by a phantomlike effective equation of state for dark energy at the present epoch. It agrees very well with observations. We demonstrate that the traditional parametrization $f=\Omega_m^\gamma$ with a quasiconstant growth index $\gamma$ is not successful in this case. Based on a power series expansion at large redshifts, we propose a different parametrization for this model: $f=\Omega_m^\gamma\left(1+\frac{b}{\ell H}\right)^\beta$, where $\beta$ and $b$ are constants. Our numerical simulations demonstrate that this new parametrization describes the growth rate with great accuracy - the maximum error being $\leq 0.1\%$ for parameter values consistent with observations.