Emulating a ACDM-like expansion on the phantom brane

In [Phys. Rev. D 80, 123003 (2009)] Schmidt suggested that dynamical dark energy (DDE) propagating on the phantom brane could mimick ACDM. Schmidt went on to derive a phenomenological expression for PDE which could achieve this. We demonstrate that while Schmidt's central premise is correct, the expression for rho(DE) derived by [Schmidt, Phys. Rev. D 80, 123003 (2009)] is flawed. We derive the correct expression for rho(DE) which leads to ACDM-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(phi). Interestingly the a-attractor based potential V(phi) proportional to coth(2)lambda phi makes braneworld expansion resemble ACDM. However the two models can easily be distinguished on the basis of density perturbations which grow at different rates on the braneworld and in ACDM.