Extremal surfaces in de Sitter spacetime

We study extremal surfaces in de Sitter space in the Poincare slicing in the upper patch, anchored on spatial subregions at the future boundary I⁺, restricted to constant boundary Euclidean time slices (focusing on strip subregions). We find real extremal surfaces of minimal area as the boundaries of past light-cone wedges of the subregions in question: these are null surfaces with vanishing area. We also find complex extremal surfaces as complex extrema of the area functional, and the area is not always real valued. In dS₄ the area is real. The area has structural resemblance with entanglement entropy in a dual conformal field theory. There are parallels with analytic continuation from the Ryu-Takayanagi expressions for holographic entanglement entropy in anti-de Sitter. We also discuss extremal surfaces in the de Sitter (dS) black brane and the de Sitter ``bluewall'' studied previously. The dS₄ black brane complex surfaces exhibit a real finite cutoff-independent extensive piece. In the bluewall geometry, there are real surfaces that go from one asymptotic universe to the other through the Cauchy horizons.