  In a recent paper [arXiv:1206.4916] by T. Padmanabhan, it was argued that our
universe provides an ideal setup to stress the issue that cosmic space is
emergent as cosmic time progresses and that the expansion of the universe is
due to the difference between the number of degrees of freedom on a holographic
surface and the one in the emerged bulk. In this note following this proposal
we obtain the Friedmann equation of a higher dimensional
Friedmann-Robertson-Walker universe. By properly modifying the volume increase
and the number of degrees of freedom on the holographic surface from the
entropy formulas of black hole in the Gauss-Bonnet gravity and more general
Lovelock gravity, we also get corresponding dynamical equations of the universe
in those gravity theories.
