Emulating $\hat{I}›$CDM-like expansion on the Phantom brane

Abstract

In [Schmidt PRD 80 123003 (2009)], the author suggested that dynamical dark energy (DDE) propagating on the phantom brane could mimick $\hat{I}›$CDM. Schmidt went on to derive a phenomenological expression for $\ddot{I}{}_{\mathrm{DE}}$ which could achieve this. We demonstrate that while Schmidt's central premise is correct, the expression for $\ddot{I}{}_{\mathrm{DE}}$ derived in Schmidt (2009) is flawed. We derive the correct expression for $\ddot{I}{}_{\mathrm{DE}}$ which leads to $\hat{I}›$CDM-like expansion on the phantom brane. We also show that DDE on the brane can be associated with a Quintessence field and derive a closed form expression for its potential $V(\ddot{I}•)$. Interestingly the $\hat{I}\pm$-attractor based potential $V(\ddot{I}•)\propto {\coth }^2\hat{I}»\ddot{I}•$ makes braneworld expansion resemble $\hat{I}›$CDM. However the two models can easily be distinguished on the basis of density perturbations which grow at different rates on the braneworld and in $\hat{I}›$CDM.

15 pages, 6 figures, published in PRD. arXiv admin note: substantial text overlap with arXiv:1709.09193