Solutions of the wave equation bounded at the Big Bang

Abstract

By solving a singular initial value problem, we prove the existence of solutions of the wave equation g φ = 0 which are bounded at the Big Bang in the Friedmann-Lemaître-Robertson-Walker cosmological models.More precisely, we show that given any function A ∈ H 3 (Σ) (where Σ = R n , S n or H n models the spatial hypersurfaces) there exists a unique solution φ of the wave equation converging to A in H 1 (Σ) at the Big Bang, and whose time derivative is suitably controlled in L 2 (Σ).Contents 1 Introduction and statement of the main result 1 2 Proof of the main result 3 A FLRW models in n + 1 dimensions 9 B Killing vector fields and the Laplacian 10

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