  This paper investigates the challenges and resolutions in computing the
entanglement entropy for the quantum field theory coupled to de Sitter (dS)
gravity along a timelike boundary. The conventional island formula, originally
designed to calculate the fine-grained entropy for a non-gravitational system
coupled to anti-de Sitter (AdS) gravity, encounters difficulties in de Sitter
gravitational spacetime, failing to provide a physically plausible extremal
island. To overcome these problems, we introduce a doubly holographic model by
embedding a dS$_2$ braneworld in an AdS$_3$ bulk spacetime. This approach
facilitates the computation of entanglement entropy through holographic
correlation functions, effectively circumventing the constraints of the island
formula. We demonstrate that the correct recipe for calculating entanglement
entropy with dS gravity involves the non-extremal island, whose boundary is
instead defined at the edge of the dS gravitational region. Our findings
indicate that, during the island phase, the entanglement wedge of the
non-gravitational bath includes the entire dS gravitational space. Using the
second variation formula, we further show that the existence of a locally
minimal surface anchored on the gravitational brane is intrinsically linked to
the extrinsic curvature of the brane.
