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Padmanabhan [arXiv:1206.4916] argues that the cosmic acceleration can beunderstood from the perspective that spacetime dynamics is an emergencephenomena. By calculating the difference between the surface degrees of freedomand the bulk degrees of freedom in a region of space, he also arrives at theFriedmann equation in a flat universe. In this paper, by modification of hisproposal, we are able to derive the Friedmann equation of theFriedmann-Robertson-Walker universewith any spatial curvature.We also extendthe study to higher-dimensional spacetime and derive successfully the Friedmannequations not only in Einstein gravity but also in Gauss-Bonnet and moregeneral Lovelock gravity with any spatial curvature. This is the firstderivation of Friedmann equations in these gravity theories in a nonflatFriedmann-Robertson-Walker universe by using the novel idea proposed byPadmanabhan. Our study indicates that the approach presented here is powerfulenough and further supports the viability of Padmanabhan's perspective ofemergence gravity.

Friedmann equations from emergence of cosmic space