High-harmonic cosmic strings and gravitational wavesTools Pazouli, Despoina (2020) High-harmonic cosmic strings and gravitational waves. PhD thesis, University of Nottingham.
AbstractIn 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 use the variational principle to derive the Einstein field equations and study the solutions of the linearized Einstein equations in the homogeneous and the non-homogeneous case in the harmonic gauge, which are the gravitational waves. We also define basic spacetime concepts and the idea of the standard cosmological model. 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. Assuming a harmonic distribution of the loops that chop off the long string network, we can calculate the average number of cusps produced per loop period from an infinitesimal spacetime volume from a network of loops. We then implement our results in the calculation of the gravitational wave signal of cusps from cosmic string loops as received on Earth. 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.
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