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arXiv · 1809.09633

Solutions of the wave equation bounded at the Big Bang

Pedro M. Girão·José Natário·Jorge Drumond Silva
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Abstract

By solving a singular initial value problem, we prove the existence of solutions of the wave equation $\Box_g\phi=0$ which are bounded at the Big Bang in the Friedmann-Lemaitre-Robertson-Walker cosmological models. More precisely, we show that given any function $A \in H^3(\Sigma)$ (where $\Sigma=\mathbb{R}^n, \mathbb{S}^n$ or $\mathbb{H}^n$ models the spatial hypersurfaces) there exists a unique solution $\phi$ of the wave equation converging to $A$ in $H^1(\Sigma)$ at the Big Bang, and whose time derivative is suitably controlled in $L^2(\Sigma)$.

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BibTeXRIS

Pedro M. Girão, José Natário, Jorge Drumond Silva. 2018-09-25. Solutions of the wave equation bounded at the Big Bang. https://doi.org/10.1088/1361-6382%2Fab09b2

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