  In this work, we show that the two proposals associated to the mutual
information of matter fields can be given for an eternal Schwarzschild black
hole in de-Sitter spacetime. These proposals also depicts the status of
associated entanglement wedges and their roleplay in obtaining the correct Page
curve of radiation. The first proposal has been give for the before Page time
scenario, 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 at
which the entanglement wedge associated to $R_{H}^{+}\cup R_{H}^{-}$ gets
disconnected 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 Page
time, when the replica wormholes are the dominating saddle-points, the mutual
information $I(B_{H}^{+}:B_{H}^{-})$ vanishes as soon as the time difference
$t_{a_{H}}-t_{b_{H}}$ equals the scrambling time. Holographically, this
reflects 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-grained
entropy of radiation as portrayed by the Page curve. We have also shown that
similar observations can be obtained for the radiation associated to the
cosmological horizon.
