Observational Evidences of Cosmic Strings

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Table of contents

1 Introduction 
2 Topological Defects 
2.1 Topological Defects Formation
2.2 Topological Classification of Defects
2.2.1 Domain Walls
2.2.2 Monopoles
2.2.3 Textures
2.3 Cosmic Strings
2.3.1 Observational Evidences of Cosmic Strings
2.4 Topological Defects in Liquid Crystals
2.4.1 Isotropic-Nematic Phase Transition
2.4.2 Nematic Liquid Crystals as a Laboratory for Cosmology
3 Geometric Aspects of Linear Defects 
3.1 Geometric Theory of Gravitation
3.1.1 Geodesic Equation
3.2 Weak Field Approximation for Regular Cosmic String
3.2.1 Gravitational Lensing
3.3 Geometric Method for Disclination
4 Wiggly String as a Waveguide 
4.1 The Wiggly Cosmic String
4.2 Propagation of Massless Fields
4.3 Propagation of Massive Fields
4.4 Optical Analogues of Spacetimes
4.4.1 An Optical Waveguide Analogue of the Wiggly String
4.5 Conclusions
5 Optical Concentrator from a Hyperbolic Metamaterial 
5.1 Hyperbolic Liquid Crystal Metamaterial
5.2 Light Trajectories in the HLCM Media
5.3 Propagating Wave Modes
5.4 Conclusions
6 Conclusions and Perspectives 
A Appendix 
A.1 Finslerian Method
A.2 Numerical Analysis
A.2.1 Finite Difference Method
A.2.2 Applying the Finite Difference Method
A.2.3 Discretization Codes
A.3 Eikonal Approximation