Formation Of Cosmic Strings Research Articles

Dynamics of cosmic string formation with emission of gravitational waves: a toy model

Starting from an extended theory of general relativity with boundary terms included, we study a toy model to describe the dynamical collapse of an infinite cylinder with positive spatial curvature from which a cosmic string is formed after collapsing, and we examine the production of gravitational waves (GW) emitted during the collapse. The background dynamics of the radial collapse is described by a massive scalar field which departs from the equilibrium when the scalar field climbs through the quadratic potential. During the collapse the radial pressure is considered as null, so that the kinetic and the potential energy densities are equaled. The components of the GW modes +,×and B, for the polarization tensor, are analytically obtained.

Percolating cosmic string loops from evaporating primordial black holes

The Pulsar timing data from NANOGrav Collaboration has regenerated interest in the possibility of observing stochastic gravitational wave background arising from cosmic strings. Standard theory of formation of cosmic strings is based on a spontaneous symmetry breaking (SSB) phase transition in the early universe, with a string network forming via the so called Kibble mechanism. This string network rapidly evolves and reaches a scaling solution with a given spectrum of string loops and long strings at any given time. This scenario necessarily requires that the entire observable Universe goes through the SSB phase transition. This would not be possible, e.g., in models of low energy inflation, where the reheat temperature is much lower than the energy scale of cosmic strings. We point out a very different possibility, where a network of even high energy scale cosmic strings can form when the temperature of the Universe is much lower. We consider local heating of plasma in the early universe by evaporating primordial black holes (PBHs). It is known that for suitable masses of PBHs, Hawking radiation of evaporating primordial black holes may re-heat the surrounding plasma to high temperatures, restoring certain symmetries locally which are broken at the ambient temperature of the Universe at that stage. Expansion of the hot plasma cools it so that the locally restored symmetry is spontaneously broken again. If this SSB supports formation of cosmic strings, then string loops will form in this region around the PBH. Further, resulting temperature gradients lead to large pressure gradients such that plasma will develop radial flow with the string loops getting stretched as they get dragged by the flow. For a finite density of PBHs of suitable masses, one will get local hot spots, each one contributing to expanding cosmic string loops. For suitable PBH density, the loops from different regions may intersect. If that happens, then intercommutation of strings can lead to percolation, leading to the possibility of formation of infinite string network, even when the entire universe never goes through the respective SSB phase transition.

Cosmic F- and D-strings from pure Yang–Mills theory

We discuss the formation of cosmic strings or macroscopic color flux tubes after the deconfinement/confinement phase transition in the pure Yang–Mills theory. Based on holographic dual descriptions, these cosmic strings can be interpreted as fundamental (F-) strings or wrapped D-branes (which we call as D-strings) in the gravity side, depending on the structure of the gauge group. In fact, the reconnection probabilities of the F- and D-strings are suppressed by factors of 1/N2 and e−cN, where c=O(1), in a large-N limit, respectively. Supported by the picture of electric–magnetic duality, we discuss that color flux tubes form after the deconfinement/confinement phase transition, just like the formation of local cosmic strings after spontaneous symmetry breaking in the weak-U(1) gauge theory. We use an extended velocity-dependent one-scale model to describe the dynamics of the string network and calculate the gravitational wave signals from string loops. We also discuss the dependence on the size of produced string loops.

Cosmic strings from pure Yang–Mills theory

We discuss the formation of cosmic strings or macroscopic color flux tubes at the phase transition from the deconfinement to confinement phase in pure Yang--Mills (YM) theory, such as $\mathrm{SU}(N)$, $\mathrm{Sp}(N)$, $\mathrm{SO}(N)$, and $\text{Spin}(N)$, based on the current understanding of theoretical physics. According to the holographic dual descriptions, the cosmic strings are dual to fundamental strings or wrapped D-branes in the gravity side depending on the structure of the gauge group, and the reconnection probability is suppressed by $\mathcal{O}({N}^{\ensuremath{-}2})$ and ${e}^{\ensuremath{-}\mathcal{O}(N)}$, respectively. The pure YM theory thus provides a simple realization of cosmic F- and D-strings without the need for a brane-inflationary scenario or extra dimension. We also review the stability of cosmic strings based on the concept of 1-form symmetry, which further implies the existence of a baryon vertex in some YM theory. We calculate the gravitational wave spectrum that is emitted from the cosmic strings based on an extended velocity-dependent one-scale model and discuss its detectability based on ongoing and planned gravitational-wave experiments. In particular, the SKA and LISA can observe gravitational signals if the confinement scale is higher than $\mathcal{O}({10}^{12})\text{ }\text{ }\mathrm{GeV}$ and $\mathcal{O}({10}^{10})\text{ }\text{ }\mathrm{GeV}$ for $\mathrm{SU}(N)$ with $N=\mathcal{O}(1)$, respectively.

The structure of cosmic strings of a U(1) gauge field for the conservation of B - L

We consider an extension of the Standard Model, where the difference between the baryon number $B$ and the lepton number $L$ is gauged with an Abelian gauge field, in order to explain the exact conservation of $B-L$. To avoid a gauge anomaly, we add a right-handed neutrino $\nu_{\rm R}$ to each fermion generation. Here it is not sterile, so the usual Majorana term is excluded by gauge invariance. We provide a mass term for $\nu_{\rm R}$ by adding a non-standard 1-component Higgs field, thus arriving at a consistent extension of the Standard Model, where the conservation of $B-L$ is natural, with a modest number of additional fields. We study the possible formation of cosmic strings by solving the coupled field equations of the two Higgs fields and the non-standard U(1) gauge field. Numerical methods provide the correspondingstring profiles, depending on the Higgs winding numbers, such that the appropriate boundary conditions in the string center and far from it are fulfilled.

Gravitational waves from melting cosmic strings

Appearance of cosmic strings in the early Universe is a common manifestation of new physics typically linked to some high energy scale. In this paper, we discuss a different situation, where a model underlying cosmic string formation is approximately scale free. String tension is naturally related to the square of the temperature of the hot primordial plasma in such a setting, and hence decreases with (cosmic) time. With gravitational backreaction neglected, the dynamicsof these melting strings in an expanding Universe is equivalent to the dynamics of constant tension strings in a Minkowski spacetime.We provide an estimate for the emission of gravitational waves from string loops. Contrary to the standard case, the resulting spectrum is markedly non-flat and has a characteristic falloffat frequencies below the peak one. The peak frequency is defined by the underlying model and lies in the range accessible by the future detectors for very weak couplings involved.

Confronting SO(10) GUTs with proton decay and gravitational waves

Grand Unified Theories (GUT) predict proton decay as well as the formation of cosmic strings which can generate gravitational waves. We determine which non-supersymmetric SO(10) breaking chains provide gauge unification in addition to a gravitational signal from cosmic strings. We calculate the GUT and intermediate scales for these SO(10) breaking chains by solving the renormalisation group equations at the two-loop level. This analysis predicts the GUT scale, hence the proton lifetime, in addition to the scale of cosmic string generation and thus the associated gravitational wave signal. We determine which SO(10) breaking chains survive in the event of the null results of the next generation of gravitational waves and proton decay searches and determine the correlations between proton decay and gravitational waves scales if these observables are measured.

Vector dark matter production from inflation with symmetry breaking

We present a scenario of vector dark matter production from symmetry breaking at the end of inflation. In this model, the accumulated energy density associated with the quantum fluctuations of the dark photon accounts for the present energy density of dark matter. The inflaton is a real scalar field while a heavy complex scalar field, such as the waterfall of hybrid inflation, is charged under the dark gauge field. After the heavy field becomes tachyonic at the end of inflation, rolling rapidly towards its global minimum, the dark photon acquires mass via the Higgs mechanism. To prevent the decay of the vector field energy density during inflation, we introduce couplings between the inflaton and the gauge field such that the energy is pumped to the dark sector. The setup can generate the observed dark matter abundance for a wide range of the dark photon's mass and with the reheat temperature around $10^{12}$ GeV. The model predicts the formation of cosmic strings at the end of inflation with the tensions which are consistent with the CMB upper bounds.

Fingerprint of low-scale leptogenesis in the primordial gravitational-wave spectrum

The dynamical generation of right-handed-neutrino (RHN) masses in the early Universe naturally entails the formation of cosmic strings that give rise to an observable signal in gravitational waves (GWs). Here, we show that a characteristic break in the GW spectrum would provide evidence for a new stage in the cosmological expansion history and a suppression of the RHN mass scale compared to the scale of spontaneous symmetry breaking. The detection of such a spectral feature would thus represent a novel and unique possibility to probe the physics of RHN mass generation in regions of parameter space that allow for low-scale leptogenesis in accord with electroweak naturalness.

Multiferroics: from the cosmically large to the subatomically small

A small but hardy core of researchers is using multiferroic materials to address fundamental questions on the nature of the universe, testing concepts in cosmology and high-energy physics. Multiferroics can be used to address fundamental questions on the nature of the universe, providing a platform to test concepts in cosmology and high-energy physics, such as the formation of cosmic strings and the existence of an electron electric dipole moment.

Black holes as beads on cosmic strings

We consider the possibility of the formation of cosmic strings with black holes as beads. We focus on the simplest setup where two black holes are formed on a long cosmic string. It turns out that in the absence of a background magnetic field and for observationally viable values for cosmic string tensions, the tension of the strut in between the black holes has to be less than the ones that run into infinity. This result does not change if a cosmological constant is present. However, if a background magnetic field is turned on, we can have stable setups where the tensions of all cosmic strings are equal. We derive the equilibrium conditions in each of these setups depending on whether the black holes are extremal or non-extremal. We obtain cosmologically acceptable solutions with solar mass black holes and an intragalactic-strength cosmic magnetic field.

Seeking string theory in the cosmos

We review the existence, formation and properties of cosmic strings in string theory, the wide variety of observational techniques that are being employed to detect them, and the constraints that current observations impose on string theory models.

Primordial Gravitational Waves from Inflation and Preheating

There are at least three cosmic backgrounds of primordial gravitational waves coming from inflation: those produced during inflation and associated with the stretching of quantum modes; those produced at the violent stage of preheating after inflation; and those associated with the self-ordering of Goldstone modes if inflation ends via a global symmetry breaking scenario, like in hybrid inflation. Each background has its own characteristic spectrum with specific features. We describe in detail the origin of extra peaks in the PGW background from preheating in the case in which inflation ends with the formation of cosmic strings due to an Abelian Higgs model after hybrid inflation. We then discuss the prospects for detecting each gravitational wave background, and distinguishing between them with a very sensitive probe, the local B-mode of the cosmic microwave background polarization.

Racetrack inflation with matter fields and cosmic strings

We consider the coupling of racetrack inflation to matter fields as realized in theD3/D7 brane system. In particular, we investigate the possibility of cosmic string formation in thissystem. We find that strings can form before or at the onset of racetrack inflation ispossible, but they are then inflated away. Furthermore, string formation at the end ofinflation is prevented by the presence of the moduli sector. As a consequence, no stringssurvive racetrack inflation.

Gaugek-vortices

We consider gauge vortices in symmetry-breaking models with a noncanonical kinetic term. This work extends our previous study on global topological $k$-defects [Phys. Rev. D 74, 085004 (2006), including a gauge field. The model consists of a scalar field with a noncanonical kinetic term, while for the gauge field the standard form of its kinetic term is preserved. Topological defects arising in such models, $k$-vortices, may have quite different properties as compared to standard vortices. This happens because an additional dimensional parameter enters the Lagrangian for the considered model---a kinetic mass. We briefly discuss possible consequences for cosmology, in particular, the formation of cosmic strings during phase transitions in the early universe and their properties.

Cosmic string formation by flux trapping

We study the formation of cosmic strings by confining a stochastic magnetic field into flux tubes in a numerical simulation. We use overdamped evolution in a potential that is minimized when the flux through each face in the simulation lattice is a multiple of the fundamental flux quantum. When the typical number of flux quanta through a correlation-length-sized region is initially about 1, we find a string network similar to that generated by the Kibble-Zurek mechanism. With larger initial flux, the loop distribution and the Brownian shape of the infinite strings remain unchanged, but the fraction of length in infinite strings is increased. A 2D slice of the network exhibits bundles of strings pointing in the same direction, as in earlier 2D simulations. We find, however, that strings belonging to the same bundle do not stay together in 3D for much longer than the correlation length. As the initial flux per correlation length is decreased, there is a point at which infinite strings disappear, as in the Hagedorn transition.

Enlarging the parameter space of standard hybrid inflation

We show that the parameter space forF-term inflation which predicts the formation of cosmic strings is larger than previouslyestimated, firstly, because realistic embeddings in GUT theories alter the standard scenario,making the inflationary potential less steep and, secondly, because the strings whichform at the end of inflation are not necessarily topologically stable down to lowscales. In shifted and smooth inflation, strings do not form at all. We also discussD-term inflation; here the possibilities are much more limited for enlarging the parameterspace.

Lorentz-breaking effects in scalar-tensor theories of gravity

In this work, we study the effects of breaking Lorentz symmetry in scalar-tensor theories of gravity taking torsion into account. We show that a space-time with torsion interacting with a Maxwell field by means of a Chern-Simons-like term is able to explain the optical activity in syncrotron radiation emitted by cosmological distant radio sources. Without specifying the source of the dilaton-gravity, we study the dilaton-solution. We analyse the physical implications of this result in the Jordan-Fierz frame. We also analyse the effects of the Lorentz breaking in the cosmic string formation process. We obtain the solution corresponding to a cosmic string in the presence of torsion by keeping track of the effects of the Chern-Simons coupling and calculate the charge induced on this cosmic string in this framework. We also show that the resulting charged cosmic string gives us important effects concerning the background radiation.The optical activity in this case is also worked out and discussed.

D-term inflation without cosmic strings.

We present a superstring-inspired version of D-term inflation that does not lead to cosmic string formation and appears to satisfy the current cosmic microwave background constraints. It differs from minimal D-term inflation by a second pair of charged superfields that makes the strings nontopological (semilocal). The strings are also Bogomol'nyi-Prasad-Sommerfield strings, so the scenario is expected to survive supergravity corrections. The second pair of charged superfields arises naturally in several brane and conifold scenarios, but its effect on cosmic string formation had not been noticed so far.

How generic is cosmic string formation in supersymmetric grand unified theories

We study cosmic string formation within supersymmetric grand unified theories (GUTs). We consider gauge groups having a rank between 4 and 8. We examine all possible spontaneous symmetry breaking patterns from the GUT down to the standard model gauge group. Assuming standard hybrid inflation, we select all the models which can solve the GUT monopole problem leading to baryogenesis after inflation, and are consistent with proton lifetime measurements. We conclude that, in all acceptable spontaneous symmetry breaking schemes, cosmic string formation is unavoidable. The strings which form at the end of inflation have a mass which is proportional to the inflationary scale. Sometimes a second network of strings form at a lower scale. Models based on gauge groups which have a rank greater than 6 can lead to more than one inflationary era; they all end by cosmic string formation.