Emulating $\Lambda$CDM-like expansion on the Phantom brane
  In [Schmidt PRD 80 123003 (2009)], the author suggested that dynamical dark
energy (DDE) propagating on the phantom brane could mimick $\Lambda$CDM.
Schmidt went on to derive a phenomenological expression for $\rho_{\rm DE}$
which could achieve this. We demonstrate that while Schmidt's central premise
is correct, the expression for $\rho_{\rm DE}$ derived in Schmidt (2009) is
flawed. We derive the correct expression for $\rho_{\rm DE}$ which leads to
$\Lambda$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 $V(\phi)$. Interestingly the $\alpha$-attractor
based potential $V(\phi) \propto \coth^2{\lambda\phi}$ makes braneworld
expansion resemble $\Lambda$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 $\Lambda$CDM.
