STABILITY OF DE SITTER SPACE AND EXPANSION AT THE CONFORMAL BOUNDARY MAURUS LEIMBACHER Abstract. Using an approach similar to [HV24], we give a new proof of the nonlinear stability arXiv:2605.03481v1 [math.AP] 5 May 2026 of de Sitter space as a solution to...
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STABILITY OF DE SITTER SPACE AND EXPANSION AT THE CONFORMAL BOUNDARY MAURUS LEIMBACHER Abstract. Using an approach similar to [HV24], we give a new proof of the nonlinear stability arXiv:2605.03481v1 [math.AP] 5 May 2026 of de Sitter space as a solution to the Einstein vacuum equations with positive cosmological constant in n + 1 dimensions, with n ≥ 3. Using the gauge freedom of the equations, we are able to prove a precise expansion of the perturbed spacetime at the conformal boundary. In n = odd spatial dimensions, the conformally rescaled metric is smooth up to the future conformal boundary and in n = even spatial dimensions it is smooth if and only if the obstruction tensor of the boundary metric vanishes; if not, then the conformally rescaled metric is log smooth at the boundary. These results also hold for asymptotically de Sitter spaces. Using the results of [FG85, FG08, RSR18, Hin24], the structure of our expansion allows us to establish a 1-1 correspondence between solutions
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