Holographic entanglement entropy and complexity for the cosmological braneworld model

In a recent study \cite{Park:2020jio}, the time-dependent entanglement entropy of the universe undergoing expansion according to various power laws has been analyzed within the framework of the braneworld model. The results of the entanglement entropy in that paper take into account only the effects of a radiation and a matter-dominated universe. In this work, we have computed the time-dependent entanglement entropy and complexity of the FLRW universe in the presence of different matter sources (radiation, matter and some exotic matter). In contrast to the approach in \cite{Park:2020jio}, all the calculations in this paper have been carried out in a perturbative manner in the framework of braneworld model of cosmology. According to this model, our universe is situated on a brane and different matter sources appear on the brane due to the back reaction of different $p$-brane gas configurations in the bulk spacetime. By considering the bulk spacetime as a black brane geometry, we have considered different blackening factors corresponding to radiation, matter, and exotic matter and calculated entanglement entropy and complexity holographically. In the braneworld model, the universe's expansion is described by the brane's time-dependent radial position. This position is determined using the second Israel junction condition for various matter sources. The time evolution of entanglement entropy and complexity is then obtained by substituting this brane position. We have also shown the dependence of entanglement entropy and complexity on the cosmological time for all the different matter-dominated universes in the early and late time eras. Even though the calculations of holographic entanglement entropy and complexity are done perturbatively, the results remain consistent with those of \cite{Park:2020jio}.