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Topological defects formed in the early stages of our universe can play a crucial role in understanding anisotropic deviations of the Friedmann Lemâitre Robertson Walker model we observe today. These defects are the result of phase transitions associated with spontaneous symmetry breaking in gauge theories at the grand unification energy scale. The most interesting defects are cosmic strings, vortex-like structures in the famous gauged U(1) abelian Higgs model with a “Mexican-hat” potential. Other defects, such as domain walls and monopoles are probably ruled out, because they should dominate otherwise the energy density of our universe. This local gauge model is the basis of the standard model of particle physics, where the Higgs-mechanism provides elementary particles with mass. It cannot be a coincidence that this model also explains the theory of superconductivity. The decay of the high multiplicity (n) super-conducting vortex into a lattice of n vortices of unit magnetic flux is energetically favourable and is experimentally confirmed. It explains the famous Meissner effect. This process could play an essential role by the entanglement of cosmic strings just after the symmetry breaking. The stability of the lattice depends critically on the parameters of the model, especially when gravity comes into play. The questions is how the imprint of the cosmic strings could be observed at present time. Up to now, no evidence is found. The recently found alignment of the spinning axes of quasars in large quasar groups on Mpc scales, could be a first indication of the existence of these cosmic strings. The temporarily broken axial symmetry will leave an imprint of a preferred azimuthal-angle on the lattice. This effect is only viable when a scaling factor is introduced. This can be realized in a warped five dimensional model. The warp factor plays the role of a dilaton field on an equal footing with the Higgs field. The resulting field equations can be obtained from a conformal invariant model. Conformal invariance, the missing symmetry in general relativity, will then spontaneously be broken, just as the Higgs field. The dilaton field, or equivalently, the warp factor, could also contribute to the expansion of the universe as it can act as a dark energy term coming from the bulk spacetime. It makes the cosmic string temporarily super-massive. This process could solve the cosmological constant and hierarchy problem. It is conjectured that the dilaton field has a dual meaning. At very early times, when the dilaton field approaches zero, it describes the small-distance limit of the model, while at later times it is a warp (or scale) factor that determines the dynamical evolution of the universe. When more data of quasars of high redshift will become available, one could prove that the alignment emerged after the symmetry breaking scale and must have a cosmological origin. The effect of the warp factor on the second-order perturbations could also be an indication of the existence of large extra dimensions.

In this work we made use of a general static cillindrically symmetric metric to find U (1) local cosmic string solutions in the context of the hybrid metric-Palatini theory of gravity in it’s scalar-tensor representation. After finding the dynamical equations for this particular case, we imposed boost invariance along t and z directions, which simplified the equations of motions, leaving only one single metric tensor component, W²(r). For an arbitrary potential V (ϕ), the solutions obtained can be put in a closed parametric form, with ϕ taken as a parameter. Several particular cases of the potential were studied, some yielding simple mathematical forms, others with only numerical solutions. In this way, we obtain a large class of novel stable stringlike solutions in the context of hybrid metric-Palatini gravity, in which the basic parameters, such as the scalar fleld, metric tensor components, and string tension, depend essentially on the initial values of the scalar fleld, and of its derivative, on the r(0) circular axis.

In this work we will explore U (1) local cosmic string solutions in the context of the generalized hybrid metric-Palatini theory of gravity in its scalar-tensor representation. Using a general static cillindrically symmetric metric to find the dynamical equations for this particular case, we will simplify the equations by imposing boost invariance along t and z directions. The physical and geometrical properties of the cosmic strings are determined by the two scalar fields, as well by an effective field potential, functionally dependent on both scalar fields. While for some forms of the potential, the dynamical equations can be solved exactly, for more general formas of the potential the solutions are found numerically. In this way, we obtain a large class of stable stringlike astrophysical configurations, whose basic parameters (string tension and radius) depend essentially on the effective field potential, and on the boundary conditions.

There has been observational evidence about spin axes of quasars in large quasar groups correlated over hundreds of Mpc. This is seen in the radio spectrum as well as in the optical range. There is not yet a satisfactory explanation of this “spooky” alignment. This alignment cannot be explained by mutual interaction at the time that quasars manifest themselves optically. A cosmological explanation could be possible in the formation of superconducting vortices (cosmic strings) in the early universe, just after the symmetry-breaking phase of the universe. We gathered from the NASA/IPAC and SIM-BAD extragalactic databases the right ascension, declination, inclination, position angle and eccentricity of the host galaxies of 3 large quasar groups to obtain the azimuthal and polar angle of the spin vectors. The alignment of the azimuthal angle of the spin vectors of quasars in their host galaxy is confirmed in the large quasar group U1.27 and compared with two other groups in the vicinity, i.e., U1.11 and U1.28, investigated by Clowes (2013). It is well possible that the azimuthal angle alignment fits the predicted azimuthal angle dependency in the theoretical model of the formation of general relativistic superconducting vortices, where the initial axially symmetry is broken just after the symmetry breaking of the scalar-gauge field.

Cosmic string networks form during cosmological phase transitions as a consequence of the Kibble mechanism. The evolution of the simplest networks is accurately described by the canonical Velocity Dependent One-Scale (VOS) model. However, numerical simulations have demonstrated the existence of significant quantities of short-wavelength propagation modes on the strings, known as wiggles, which motivated the recent development of a wiggly string extension of the VOS. Here we summarize recent progress in the physical interpretation of this model through a systematic study of the allowed asymptotic scaling solutions of the model. The modeling mainly relies on three mechanisms: the universe’s expansion rate, energy transfer mechanisms (e.g., the production of loops and wiggles), and the choice of the scale in which wiggles are coarse-grained. We consider the various limits in which each mechanism dominates and compare the scaling solutions for each case, in order to gain insight into the role of each mechanism in the overall behavior of the network. Our results show that there are three scaling regimes for the wiggliness, consisting of the well-known Nambu-Goto solution, and non-trivial regimes where the amount of wiggliness can grow as the network evolves or, for specific expansion rates, become a constant. We also demonstrate that full scaling of the network is more likely in the matter era than in the radiation epoch, in agreement with numerical simulations.

The canonical velocity-dependent one-scale (VOS) model for cosmic string evolution contains a number of free parameters which cannot be obtained ab initio. Therefore it must be calibrated using high resolution numerical simulations. We exploit our state of the art graphically accelerated implementation of the evolution of local Abelian-Higgs string networks to provide a statistically robust calibration of this model. In order to do so, we will make use of the largest set of high resolution simulations carried out to date, for a variety of cosmological expansion rates, and explore the impact of key numerical choices on model calibration, including the dynamic range, lattice spacing, and the choice of numerical estimators for the mean string velocity. This sensitivity exploration shows that certain numerical choices will indeed have consequences for observationally crucial parameters, such as the loop chopping parameter. To conclude, we will also briefly illustrate how our results impact observational constraints on cosmic strings.

We present results from adaptive mesh refinement (AMR) simulations of global cosmic strings. Using the public code, GRChombo, we perform a quantitative investigation of the dynamics of single sinusoidally displaced string configurations. We study a wide range of string energy densities μ ∝ ln λ, defined by the string width parameter λ over two orders of magnitude. We investigate the resulting massless (Goldstone boson or axion) and massive (Higgs) radiation signals, using quantitative diagnostic tools to determine the eigenmode decomposition. Given analytic radiation predictions for global Nambu-Goto strings, we compare the oscillating string decay with a backreaction model accounting for radiation energy losses, finding excellent agreement. We establish that backreaction decay is accurately characterised by the inverse square of the amplitude being proportional to the inverse tension μ for 3 ≲ λ ≲ 100. The investigation of massive radiation at small to intermediate amplitudes finds evidence that it is suppressed exponentially relative to the preferred massless channel with a $\sqrt{\lambda }$ dependence in the exponent. We conclude that analytic radiation modelling in the thin-string (Nambu-Goto) limit provides the appropriate cosmological limit for global strings.

In the main article [CQG 38 (2021) 055003], a new “canonical” form for the Lewis metrics of the Weyl class has been obtained, depending only on three parameters — Komar mass and angular momentum per unit length, plus the angle deficit — corresponding to a coordinate system fixed to the “distant stars” and an everywhere timelike Killing vector field. Such form evinces the local but non-global static character of the spacetime, and striking parallelisms with the electromagnetic analogue. We discuss here its generality, main physical features and important limits (the Levi-Civita static cylinder, and spinning cosmic strings). We contrast it on geometric and physical grounds with the Kerr spacetime — as an example of a metric which is locally non-static.

We present a numerical solution of a stationary 5-dimensional spinning cosmic string in the Einstein-Yang-Mills (EYM) model, where the extra bulk coordinate ψ is periodic. It turns out that when g_ψψ approaches zero, i.e., a closed time-like curve (CTC) would appear, the solution becomes singular. We also investigated the geometrical structure of the static 5D cosmic string. Two opposite moving 5D strings could, in contrast with the 4D case, fulfil the Gott condition for CTC formation.

A rotating black hole threaded by an infinitely long cosmic string is studied in the framework of the Abelian Higgs model. We show that contrary to a common belief in the presence of rotation the backreaction of the string does not induce a simple conical deficit. This leads to new distinct features of the Kerr–string system such as modified ISCO or shifted ergosphere, though these effects are most likely outside the range of observational precision. For an extremal rotating black hole, the system exhibits a first-order phase transition for the gravitational Meissner effect: small black holes exhibit a flux-expelled solution, with the gauge and scalar field remaining identically in their false vacuum state on the event horizon, whereas the horizon of large black holes is pierced by the vortex.

We present a U(1) gauge cosmic string solution on a warped 5-dimensional space time, where we solved the effective 4-dimensional equations modified by the projection of the Weyl tensor on the brane together with the junction and boundary conditions. Where the mass per unit length of the string in the bulk can be of order of the Planck scale, in the brane it will be warped down to unobservable GUT scale. It turns out that the induced 4-dimensional space time does not show asymptotic conical behavior as in the 4D counterpart model. So there is no angle deficit and the space time seems to be unphysical at finite distance from the core of the string. This could explain the absence of observational evidence of the lensing effect cosmic strings would produce and could have consequences for the (2+1)-dimensional related models.

At its very beginning, the universe is believed to have grown exponentially in size via the mechanism of inflation. The almost scale-invariant density perturbation spectrum predicted by inflation is strongly supported by cosmological observations, in particular the cosmic microwave background (MB) radiation. However, the universe’s precise inflationary scenario remains a profound problem for cosmology and for fundamental physics. String theory, the most-studied theory as the final physical theory of nature, should provide an answer to this question. Some of the proposals on how inflation is realized in string theory are reviewed. Since everything is made of strings, some string loops of cosmological sizes are likely to survive in the hot big bang that followed inflation. They appear as cosmic strings, which can have intricate properties. Because of the warped geometry in flux compactification of the extra spatial dimensions in string theory, some of the cosmic strings may have tensions substantially below the Planck or string scale. Such strings cluster in a manner similar to dark matter leading to hugely enhanced densities. As a result, numerous fossil remnants of the low tension cosmic strings may exist within the galaxy. They can be revealed through the optical lensing of background stars in the near future and studied in detail through gravitational wave emission. We anticipate that these cosmic strings will permit us to address central questions about the properties of string theory as well as the birth of our universe.