
Title
The effect of expansion and dispersion on waves in cosmological spacetimes
Abstract
The standard cosmological models describing a homogeneous and isotropic universe in general relativity are represented by the FLRW spacetimes. A step toward understanding the dynamics of the Einstein equation near the FLRW spacetimes is to study the scalar wave equation on the FLRW spacetime and derive robust quantitative estimates.
In this talk, after a brief introduction, we consider the wave equation on cosmological FLRW spacetimes with the expansion rate in the decelerated regime. We then present upcoming work that develops robust techniques, including energy boundedness and the Morawetz estimate, by utilizing the expansion properties of the metric and the dispersive characteristics of waves. Finally, we explain how these estimates lead to a new proof of the decay of waves in the FLRW spacetimes.
Please note that the seminar will take place in person in room 144 of Huxley Building.