  Recently, a novel idea about our expanding Universe was proposed by T.
Padmanabhan [arXiv:1206.4916]. He suggested that the expansion of our Universe
can be thought of as the emergence of space as cosmic time progresses. The
emergence is governed by the basic relation that the increase rate of Hubble
volume is linearly determined by the difference between the number of degrees
of freedom on the horizon surface and the one in the bulk. In this paper,
following this idea, we generalize the basic relation to derive the Friedmann
equations of an $(n+1)$-dimensional Friedmann-Robertson-Walker universe
corresponding to general relativity, Gauss-Bonnet gravity, and Lovelock
gravity.
