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In this work, we show that the two proposals associated to the mutualinformation of matter fields can be given for an eternal Schwarzschild blackhole in de-Sitter spacetime. These proposals also depicts the status ofassociated entanglement wedges and their roleplay in obtaining the correct Pagecurve of radiation. The first proposal has been give for the before Page timescenario, which shows that the mutual information $I(R_{H}^{+}:R_{H}^{-})$vanishes at a certain value of the observer's time $t_{b_{H}}=t_{H}$ (where$t_{H}\ll \beta_{H}$). We claim that this is the Hartman-Maldacena time atwhich the entanglement wedge associated to $R_{H}^{+}\cup R_{H}^{-}$ getsdisconnected and the fine-grained radiation entropy has the form $S(R_{H})\sim\log(\beta_{H})$. The second proposal depicts the fact that just after the Pagetime, when the replica wormholes are the dominating saddle-points, the mutualinformation $I(B_{H}^{+}:B_{H}^{-})$ vanishes as soon as the time difference$t_{a_{H}}-t_{b_{H}}$ equals the scrambling time. Holographically, thisreflects that the entanglement wedge associated to $B_{H}^{+}\cup B_{H}^{-}$jumps to the disconnected phase at this particular time-scale. Furthermore,these two proposals lead us to the correct time-evolution of the fine-grainedentropy of radiation as portrayed by the Page curve. We have also shown thatsimilar observations can be obtained for the radiation associated to thecosmological horizon.

Mutual information of subsystems and the Page curve for Schwarzschild de-Sitter black hole