Cosmology with the CFT-radiation matter

We review the relation between entropy bounds to rewrite Friedmann equation on the brane in terms of three entropy bounds: Bekenstein-Verlinde ($S_{BV}$); Bekenstein-Hawking bound ($S_{BH}$); Hubble bound ($S_H$). For a strongly coupled conformal field theory (CFT) with a dual 5-dimensional anti de Sitter Schwarzschild (AdSS$_5$) black hole, we can easily establish the connection between the Cardy-Verlinde formula on the CFT side and the entropy representation of Friedmann equation in cosmology. In this case its cosmological evolution for entropy is given by the semi-circle. However, for the matter-dominated case, we find that the cosmological evolution diagram takes a different form of the cycloid. Here we propose two different entropy relations for matter-dominated case. It turns out that the Verlinde's entropy relation so restricted that it may not be valid for the matter-dominated universe.