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 $f=\hat{I}{\text{c◯}}_m^3$ with a quasiconstant growth index ${\hat{I}}^3$ is not successful in this case. Based on a power series expansion at large redshifts, we propose a different parametrization for this model: $f=\hat{I}{\text{c◯}}_m^3{\left(1+\frac{b}{\ell H}\right)}^2$, where ${\hat{I}}^2$ and $b$ are constants. Our numerical simulations demonstrate that this new parametrization describes the growth rate with great accuracy - the maximum error being $\le 0.1\%$ for parameter values consistent with observations.

21 pages, 5 figures, published version