Emergence of spacetime dynamics in entropy corrected and braneworld models

A very interesting new proposal on the origin of the cosmic expansion was recently suggested by Padmanabhan [arXiv:1206.4916]. He argued that the difference between the surface degrees of freedom and the bulk degrees of freedom in a region of space drives the accelerated expansion of the universe, as well as the standard Friedmann equation through relation $% \triangle V=\triangle t(N_{\mathrm{sur}}-N_{\mathrm{bulk}})$. In this paper, we first present the general expression for the number of degrees of freedom on the holographic surface, $N_{\mathrm{sur}}$, using the general entropy corrected formula $S=\frac{A}{4 L_{p}^2}+s(A)$. Then, as two example, by applying the Padmanabhan's idea we extract the corresponding Friedmann equations in the presence of power-law and logarithmic correction terms in the entropy. We also extend the study to RS II and DGP branworld models and derive successfully the correct form of the Friedmann equations in these theories. Our study further supports the viability of Padmanabhan's proposal.