Cosmic adventures in stringland : scattering of bosonic and fermionic fields in gravitating cosmic string spacetimes

Abstract

Cosmic strings are line-like topological defects expected to have formed during cosmological phase transitions in the early universe when the Higgs field acquired a non-vanishing expectation value. Because of being thin, on a cosmological scale, their gravitational effects are usually studied

using the wire approximation, in which the string has a negligible width. Although the wire approx- imation seems reasonable in the cosmological context, local gravitational interaction with matter

fields can be significant when considering a non-vanishing radius. Generally, the spacetime of a gravitating vortex is flat at the center, has a localized curvature at some finite distance from the core, and is flat and conical far from the center. The conical structure is characterized by an angular variable ranging from 0 to less than 2π, i.e., the space has an angular deficit. This work shows that when considering a scalar field scattering in a gravitating cosmic string spacetime, the standard partial-wave approach’s scattering amplitude is singular. In order to avoid the divergence caused by the spacetime asymptotically conical structure, we propose a modification of the asymptotic ansatz

in the partial-wave formalism and find the corrections in the phase-shift and total scattering cross- section. We also developed a toy model for the spacetime metric of a cosmic string and showed how

local interaction with the vortex gauge field affects the scalar field total cross-section. Then we apply this formalism to a Dirac field and show the explicit formula for the fermionic total cross-section. Finally, we study the scattering of bosonic and fermionic fields in the spacetime of an abelian and a nonabelian gravitating cosmic strings and show that the cross-sections have damped oscillations. In order to understand the origin of this behavior, we used the aforementioned toy model to show that the spacetime particular asymptotical structure causes the observed oscillations.