Boundedness and decay of waves on spatially flat decelerated FLRW spacetimes

2025/05/22 by Mahdi Haghshenas, Haghshenas, Mahdi · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2505.16794

openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the linear wave equation on a class of spatially homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes in the decelerated regime with spatial topology ℝ³. Employing twisted t-weighted multiplier vector fields, we establish uniform energy bounds and derive integrated local energy decay estimates across the entire range of the decelerated expansion regime. Furthermore, we obtain a hierarchy of r^p-weighted energy estimates à la the Dafermos-Rodnianski r^p-method, which leads to energy decay estimates. As a consequence, we demonstrate pointwise decay estimates for solutions and their derivatives. In the wave zone, this pointwise decay is optimal in the "radiation" and "sub-radiation" cases, and almost optimal around the radiation case.

Citations

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Cited by

• Future stability of solutions of the Einstein-nonlinear scalar field system with decelerated expansion

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• The wave equation near flat Friedmann-Lemaître-Robertson-Walker and Kasner Big Bang singularities
• Pointwise decay for the wave equation on nonstationary spacetimes