Versatile parametrization of the perturbation growth rate on the phantom
  brane
  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.
