Abstract:
We study field theoretical models for cosmic strings with flat directions in curved space-time. More precisely, we consider minimal models with semilocal, axionic and tachyonic strings, respectively. In flat space-time, the string solutions of these models have a flat direction, i.e., a uniparametric family of configurations with the same energy exists which is associated to a zero mode. We prove that the zero mode survives coupling to gravity, and study the role of the flat direction when coupling the strings to gravity. Even though the total energy of the solution is the same, and thus the global properties of the family of solutions remains unchanged, the energy density, and therefore the gravitational properties, are different. The local structure of the solutions depends strongly on the value of the parameter describing the flat direction; for example, for supermassive strings, the value of the free parameter can determine the size of the universe.

Abstract:
Cosmic strings are considered in two types of gauged sigma models, which generalize the gravitating Abelian Higgs model. The two models differ by whether the U(1) kinetic term is of the Maxwell or Chern-Simons form. We obtain the self-duality conditions for a general two-dimensional target space defined in terms of field dependent "dielectric functions". In particular, we analyze analytically and numerically the equations for the case of O(3) models (two-sphere as target space), and find cosmic string solutions of several kinds as well as gravitating vortices. We classify the solutions by their flux and topological charge. We note an interesting connection between the Maxwell and Chern-Simons type models, which is responsible for simple relations between the self-dual solutions of both types. There is however a significant difference between the two systems, in that only the Chern-Simons type sigma model gives rise to spinning cosmic vortices.

Abstract:
In this work we study equations describing Abelian vortices on a Riemann surface with back reaction of the metric. The gravitating vortex equations are derived by dimensional reduction of the K\"ahler--Yang--Mills equations on the product of the complex projective line with a Riemann surface, and inherit their moment map interpretation. Applying the general theory for the K\"ahler--Yang--Mills equations, we give evidence of an analogue of the Donaldson--Uhlembeck--Yau Theorem for gravitating vortices --- commonly referred to as a Hitchin--Kobayashi correspondence. As a particular case of the gravitating vortex equations on $\mathbb{P}^1$ we find the Einstein--Bogomol'nyi equations, whose solutions correspond to Nielsen--Olesen cosmic strings in the Bogomol'nyi phase. Using an existence theorem by Yisong Yang, our main result implies a Hitchin--Kobayashi correspondence for the Einstein--Bogomol'nyi equations. In particular, we prove a conjecture by Yang about the non-existence of cosmic strings on $\mathbb{P}^1$ superimposed at a single point.

Abstract:
We present the "classical" Nielsen-Olesen vortex solution on a warped five dimensional space time, where we solved the effective four-dimensional equations from the five-dimensional equations together with the junction and boundary conditions. Four dimensional cosmic strings show some serious problems concerning the mechanism of string smoothing related to the string mass per unit length, $G\mu \leq 10^{-6}$. Moreover, there is no observational evidence of axially symmetric lensing effect caused by cosmic strings. Also super-massive cosmic strings ($G\mu\gtrsim 1$), predicted by superstring theory, possess some problems. They are studied because the universe may have undergone phase transitions at scales much higher than the GUT scale. But $G\mu \gtrsim 1$ is far above observational bounds, so one needs an inflationary scenario to smooth them out. Further, it is believed that these super-massive strings could never have extended to macroscopic size. Brane-world models could overcome these problems. $G\mu$ could be warped down to GUT scale, even if its value was at the Planck scale. In our warped cosmic string model, where the string mass per unit length in the bulk can be of order of the Planck scale, we find that the four dimensional brane space time is exponential warped down. Moreover, asymptotically the induced four dimensional space time doesn't show conical behavior. So there is no angle deficit compared to its value in the bulk and the space time seems to be un-physical, at least under fairly weak assumptions on the stress-energy tensor and without a positive brane tension. The results are confirmed by numerical solutions of the field equations.

Abstract:
We discuss cosmic Nielsen-Olesen strings in space-times endowed with a positive cosmological constant. For the cylindrically symmetric, static free cosmic string, we discuss the contribution of the cosmological constant to the angle deficit, and to the motion of the null/timelike geodesics. For a non-gravitating cosmic string in a Schwarzschild-de Sitter space-time, we discuss how a thin string can pierce the two horizons. We also present a metric which describes the exterior of a self gravitating thin string present in the Schwarzschild-de Sitter space-time.

Abstract:
We study field theoretical models for cosmic (p,q)-superstrings in a curved space-time. We discuss both string solutions, i.e. solutions with a conical deficit, but also so-called Melvin solutions, which have a completely different asymptotic behaviour. We show that globally regular gravitating (p,q)-strings exist only in a finite domain of the parameter space and study the dependence of the domain of existence on the parameters in the model. We find that due to the interaction between strings, the parameter range where string solution exist is wider than for non-interacting strings.

Abstract:
Cosmic strings, a hot subject in the 1980's and early 1990's, lost its appeal when it was found that it leads to inconsistencies in the power spectrum of the measured cosmic microwave background temperature anisotropies. However, topological defects in general, and cosmic strings in particular, are deeply rooted in the framework of grand unified theories. Indeed, it was shown that cosmic strings are expected to be generically formed within supersymmetric grand unified theories. This theoretical support gave a new boost to the field of cosmic strings, a boost which has been recently enhanced when it was shown that cosmic superstrings (fundamental or one-dimensional Dirichlet branes) can play the role of cosmic strings, in the framework of braneworld cosmologies. To build a cosmological scenario we employ high energy physics; inflation and cosmic strings then naturally appear. Confronting the predictions of the cosmological scenario against current astrophysical/cosmological data we impose constraints on its free parameters, obtaining information about the high energy physics we employed. This is a beautiful example of the rich and fruitful interplay between cosmology and high energy physics.

Abstract:
Cosmic strings are linear concentrations of energy that form whenever phase transitions in the early universe break axial symmetries as originally shown by Kibble. They are the result of frustrated order in the quantum fields responsible for elementary particles and their interactions. For about two decades, motivation for their study was provided by the possibility that they could be behind the density inhomogeneities that led to the observed large-scale structures in the universe. Precision observations, particularly of the cosmic microwave background radiation, have limited strings to a sub-dominant role in structure formation. More recently, interest has been revived with the realization that there may be strong links between field theory cosmic strings and fundamental strings. The latter are the supposed ultimate building blocks of matter, and in their original context of superstring theory were thought to be microscopic. However, in its modern version---sometimes referred to as M-theory---it is possible and perhaps even mandatory to have macroscopic (cosmological-sized) fundamental strings...

Abstract:
In these lectures, I review the current status of cosmic strings and cosmic superstrings. I first discuss topological defects in the context of Grand Unified Theories, focusing in particular in cosmic strings arising as gauge theory solitons. I discuss the reconciliation between cosmic strings and cosmological inflation, I review cosmic string dynamics, cosmic string thermodynamics and cosmic string gravity, which leads to a number of interesting observational signatures. I then proceed with the notion of cosmic superstrings arising at the end of brane inflation, within the context of brane-world cosmological models inspired from string theory. I discuss the differences between cosmic superstrings and their solitonic analogues, I review our current understanding about the evolution of cosmic superstring networks, and I then briefly describe the variety of observational consequences, which may help us to get an insight into the stringy description of our Universe.

Abstract:
The topic of cosmic strings provides a bridge between the physics of the very small and the very large. They are predicted by some unified theories of particle interactions. If they exist, they may help to explain some of the largest-scale structures seen in the Universe today. They are `topological defects' that may have been formed at phase transitions in the very early history of the Universe, analogous to those found in some condensed-matter systems --- vortex lines in liquid helium, flux tubes in type-II superconductors, or disclination lines in liquid crystals. In this review, we describe what they are, why they have been hypothesized and what their cosmological implications would be. The relevant background from the standard models of particle physics and cosmology is described in section 1. In section 2, we review the idea of symmetry breaking in field theories, and show how the defects formed are constrained by the topology of the manifold of degenerate vacuum states. We also discuss the different types of cosmic strings that can appear in different field theories. Section 3 is devoted to the dynamics of cosmic strings, and section 4 to their interaction with other fields. The formation and evolution of cosmic strings in the early Universe is the subject of section 5, while section 6 deals with their observational implications. Finally, the present status of the theory is reviewed in section 7.