High-harmonic cosmic strings and gravitational waves
  In this thesis we describe high-harmonic cosmic string loops in a general
relativistic context, and study the implications of high-harmonic content for
the predicted gravitational wave signal from cosmic string networks. Initially,
we introduce the variational principle, spacetime concepts and other
mathematical tools that we will need for the calculations in the following
chapters. We introduce the FLRW universe and the $\Lambda CDM$ universe. We
then describe the Nambu-Goto cosmic string in a curved spacetime, its equations
of motion and its energy-momentum tensor. Fixing the spacetime to be flat, and
fixing the gauge, we find the motion of the cosmic string and we present and
discuss special solutions. Using the odd-harmonic family of cosmic string
loops, we calculate the number of cusps per period and the values of the second
derivatives of the left- and right-moving harmonic modes at the cusp, and study
their dependence on the harmonic order. We then develop a toy model that
calculates the stable daughter loops produced from a parent loop using a
statistical approach based on a binary tree description of the loop chopping.
We also use the toy model to calculate the average number of cusps produced
from a system of loops that self intersect over their course of existence. We
derive the gravitational waveform emitted from a cusp as observed away from the
cusp, in any direction of observation. We then propagate this result in an FLRW
spacetime to reach an expression of its amplitude on Earth. Assuming two
different cosmic string network models, we implement our above mentioned
high-harmonic results to find the amplitude of the signal and the rate at which
these signals reach an observer on Earth.
