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The expansion law proposed by Padmanabhan suggests that the evolution of thevolume of the horizon is due to the difference between the degrees of freedomon the horizon and the degrees of freedom in the bulk enclosed by the horizon.In formulating this law, Padmanabhan used the temperature, $T=H/2\pi$, for adynamical expansion. In this work, we modified the expansion law usingKodama-Hayward temperature, the dynamical temperature, for the horizon, firstin (3+1) Einstein's gravity and extended it to higher order gravity theoriessuch as (n+1) Einstein gravity, Gauss-Bonnet gravity, and more general Lovelockgravity. Contrary to the conventional approach, we expressed degrees of freedomof the horizon in terms of the surface energy of the horizon. Also, we haveexpressed modified expansion law in terms of cosmic components. It then turnsout that it is possible to express the modified expansion law in a form as if$T=H/2\pi$ is the temperature of the dynamical horizon.

Modified expansion law with Kodama-Hayward temperature for the horizon