  A $D3-$ brane with non-zero energy density is considered as the boundary of a
five dimensional Schwarzschild anti de Sitter bulk background. Taking into
account the semi-classical corrections to the black hole entropy that arise as
a result of the self-gravitational effect, and employing the AdS/CFT
correspondence, we obtain the self-gravitational correction to the first
Friedmann-like equation. The additional term in the Hubble equation due to the
self-gravitational effect goes as $a^{-6}$. Thus, the self-gravitational
corrections act as a source of stiff matter contrary to standard FRW cosmology
where the charge of the black hole plays this role.
