Vacuum decay is a quantum mechanical process which describes the tunnelling of the Universe from the false vacuum state to the true vacuum of the theory, leading to the breaking of gauge symmetries and separating forces which once were unified. This occurs through the nucleation of bubbles of the true vacuum which grow and fill up the entire spacetime continuum. This thesis visits topics on vacuum decay and presents new original findings. We study the effects of Goldstone modes on the stability of the vacuum in a U(1) theory for a complex scalar field. The dynamics of the field resemble those of Keplerian motion in the presence of time-dependent friction, whose equations of motion imply a conserved quantity, L, reminiscent of conserved angular momentum. We show that divergences at the origin of coordinates render any solution in flat spacetime physically unattainable. We then show that, in a spacetime punctured at the origin of coordinates, it is possible to obtain finite-action solutions to the equations of motion, which correspond to the size of the hole, which in turn determines the tunnelling point and the value of the conserved quantity L. We find that the vacuum is comparatively short-lived for all possible orderings in which the false and true vacua are placed in the potential. We also show how Goldstone modes provide the necessary energy to overcome drag forces yielding finite-action solutions for any potential, including those for which no such solutions exist for real scalar fields. Gravitational waves sourced by sound waves resulting from the collision of bubbles of the true vacuum may serve as evidence for cosmological phase transitions in the early Universe. Therefore, we developed a mathematical formalism which aims to estimate the distribution of bubble lifetimes, which helps us to predict the shape of the resultant gravitational wave power spectrum.

Vacuum Decay: Goldstone modes and Bubble Lifetime

Hijazi, M. (Author). 1 Aug 2023

Student thesis: Phd