2019/09/03 by José Natário, Jose Natario, Natario, Jose +2
Mathematics · Physics and Astronomy · #35B40 #35L15 #58J45 (Primary) #83C57 #83F05 (Secondary) #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Classical mechanics #Cosmology #Cosmology and Gravitation Theories #Dark energy #De Sitter universe #FOS: Mathematics #FOS: Physical sciences #Friedmann equations #Friedmann–Lemaître–Robertson–Walker metric #General Relativity and Quantum Cosmology (gr-qc) #Inflation (cosmology) #Klein–Gordon equation #Mathematical Physics (math-ph) #Mathematical physics #Metric expansion of space #Physics #Quantum mechanics #Spacetime #Theoretical physics #Universe #gr-qc #math-ph #math.AP #math.MP #msc:35B40 #msc:35L15 #msc:58J45 #msc:83C57 #msc:83F05
paper · pdf · doi:10.48550/arxiv.1909.01292
54 pages, 4 figures. Four extra references added after a first round of review
openalex publication_date 2019/09/03 · arxiv created 2021/08/01 · arxiv updated 2021/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The decay of solutions to the Klein-Gordon equation is studied in two expanding cosmological spacetimes, namely the de Sitter universe in flat Friedmann-Lemaître-Robertson-Walker (FLRW) form, and the cosmological region of the Reissner-Nordström-de Sitter (RNdS) model. Using energy methods, for initial data with finite higher order energies, decay rates for the solution are obtained. Also, a previously established decay rate of the time derivative of the solution to the wave equation, in an expanding de Sitter universe in flat FLRW form, is improved, proving Rendall's conjecture. A similar improvement is also given for the wave equation in the cosmological region of the RNdS spacetime.