Abstract
Topological defects predicted by extensions of general relativity can manifest in gravitational-wave observations on Earth. Future broadband gravitational-wave observations show promise of constraining such models. Analytical models can in the ultimate consequence access certain parameter spaces and dynamical ranges that are prohibitively expensive to simulate. As a toy example, we present symmetron domain walls formed at redshift ∼ 2 (around ten billion years ago) with structural ripples and investigate how gravitational radiation carries information about the symmetry-breaking theory. We derive the dynamics in the thin-wall limit from the Nambu–Goto action, and analytically solve the equation of motion for a small perturbation to planar walls during phase transition, when the surface energy density is time-dependent. These results are compared to the full field theory with deterministic simulations. We find good qualitative correspondence between the thin-wall approximation and cosmological simulations. The wall positions from the two theories have average difference ∼ 7% of initial perturbation magnitude when this is ≲ 10% of the simulation box size. Lack of analytical summary statistics for the prototype makes comparative gravitational-wave analyses complicated, but we provide a superficial presentation of the results and discuss specifics of potential ways forward. We present a protocol for reducing scalar-field oscillations to perform controlled toy-model simulations.
Supervisor: Professor David F. Mota, Institute of Theoretical Astrophysics, UiO
Intern. assessor: Professor Øystein Elgarøy, Institute of Theoretical Astrophysics, UiO
Extern. assessor: Professor Anders Tranberg, Department of Mathematics and Physics, UiS