  Padmanabhan [arXiv:1206.4916] argues that the cosmic acceleration can be
understood from the perspective that spacetime dynamics is an emergence
phenomena. By calculating the difference between the surface degrees of freedom
and the bulk degrees of freedom in a region of space, he also arrives at the
Friedmann equation in a flat universe. In this paper, by modification of his
proposal, we are able to derive the Friedmann equation of the
Friedmann-Robertson-Walker universewith any spatial curvature.We also extend
the study to higher-dimensional spacetime and derive successfully the Friedmann
equations not only in Einstein gravity but also in Gauss-Bonnet and more
general Lovelock gravity with any spatial curvature. This is the first
derivation of Friedmann equations in these gravity theories in a nonflat
Friedmann-Robertson-Walker universe by using the novel idea proposed by
Padmanabhan. Our study indicates that the approach presented here is powerful
enough and further supports the viability of Padmanabhan's perspective of
emergence gravity.
