Emulating $\Lambda$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 $\Lambda$CDM. Schmidt went on to derive a phenomenological expression for ${\rho }_{\mathrm{DE}}$ which could achieve this. We demonstrate that while Schmidt's central premise is correct, the expression for ${\rho }_{\mathrm{DE}}$ derived in Schmidt (2009) is flawed. We derive the correct expression for ${\rho }_{\mathrm{DE}}$ 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 $V(\varphi )$. Interestingly the $\alpha$-attractor based potential $V(\varphi )\propto {\coth }^2\lambda \varphi$ 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.

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

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