Boundedness and decay of waves on spatially flat decelerated FLRW spacetimes
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909620297007104 |
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| author | Haghshenas, Mahdi |
| author_facet | Haghshenas, Mahdi |
| contents | 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 $\mathbb{R}^3$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16794 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundedness and decay of waves on spatially flat decelerated FLRW spacetimes Haghshenas, Mahdi General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs 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 $\mathbb{R}^3$. 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. |
| title | Boundedness and decay of waves on spatially flat decelerated FLRW spacetimes |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2505.16794 |