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In this paper we study Weyl fermions in a family of G\"odel-type geometries in Einstein general relativity. We also consider that these solutions are embedded in a topological defect background. We solve the Weyl equation and find the energy eigenvalues and eigenspinors for all three cases of G\"odel-type geometries where a topological defect is passing through them. We show that the presence of a topological in these geometries contributes to modification of the spectrum of energy. The energy zero modes for all three cases of the G\"odel geometries are discussed., Comment: 19 pages. Revised version accepted for publication in IJMPD

In this paper we consider modification of electronic properties of graphene-based topological insulator in the presence of wedge disclination and magnetic field by adopting the Kane-Mele model with intrinsic spin-orbit coupling. Using the properly defined Dirac-Weyl equation for this system, an exact solution for the Landau levels is obtained. The influence of the topological defect on the evolution of Landau levels is discussed., Comment: 16 pages, 3 figures, version published in Annals of Physics

In this paper, we analyze Dirac fermions in G\"odel-type background space-times with torsion. We also consider the G\"odel-type spacetimes embedded in a topological defect background. We show that relativistic bound states solutions to the Dirac equation can be obtained by dealing with three cases of the G\"odel-type solutions with torsion, where a cosmic string passes through these three cases of the space-time. We obtain the relativistic energy levels for all cases of the G\"odel-type solutions with torsion with a cosmic string, where we show that there exists an analogy with the Landau levels for Dirac particles. We also show that the presence of torsion in the space-time yields new contributions to the relativistic spectrum of energies and that the presence of the topological defect modifies the degeneracy of the relativistic energy levels., Comment: 26 pages, no figures, version published in EPJPlus

We consider a class of topological defects in $(1,1)$-dimensions with a deformed $\phi^4$ kink structure whose stability analysis leads to a Schr\"odinger-like equation with a zero-mode and at least one vibrational (shape) mode. We are interested in the dynamics of kink-antikink collisions, focusing on the structure of two-bounce windows. For small deformation and for one or two vibrational modes, the observed two-bounce windows are explained by the standard mechanism of a resonant effect between the first vibrational and the translational modes. With the increasing of the deformation, the effect of the appearance of more than one vibrational mode is the gradual disappearance of the initial two-bounce windows. The total suppression of two-bounce windows even with the presence of a vibrational mode offers a counterexample from what expected from the standard mechanism. For even larger deformation, some two-bounce windows reappear, but with a non-standard structure., Comment: 13 pages, 6 figures

In this work we analyze a system consisting in two-dimensional position-dependent massive particles in the presence of a Morse-like potential in two spatial dimensions. We obtain the exact wavefunctions and energies for a complete set of eigenstates for a given dependence of the mass with the spatial variables.

In this work we present a new class of real scalar field models admitting strongly interactive kink solutions. Instead of the usual exponential asymptotic behavior these topological solutions exhibit a power-law one. We investigate the interaction force between a pair of kink/anti-kink solutions both analytically and numerically, by integrating the time dependent field equations of the model. Furthermore, working within the first-order framework, we analyze the linear stability of these solutions. The stability analysis leads to Sch\"odinger-like equations with potentials which, despite admitting no bound states, lead to strong resonance peaks. We argue that these properties are important for some possible physical applications., Comment: 9 pages, 8 figures

In this paper we develop a common theoretical framework for the dynamics of thin featureless interfaces. We explicitly demonstrate that the same phase field and velocity dependent one-scale models characterizing the dynamics of relativistic domain walls, in a cosmological context, can also successfully describe, in a friction dominated regime, the dynamics of nonrelativistic interfaces in a wide variety of material systems. We further show that a statistical version of von Neumann's law applies in the case of scaling relativistic interface networks, implying that, although relativistic and nonrelativistic interfaces have very different dynamics, a single simulation snapshot is not able to clearly distinguish the two regimes. We highlight that crucial information is contained in the probability distribution function for the number of edges of domains bounded by the interface network and explain why laboratory tests with nonrelativistic interfaces can be used to rule out cosmological domain walls as a significant dark energy source., Comment: 5 pages, 3 figures

In this work we investigate the duality linking standard and tachyon scalar field cosmologies. We determine the transformation between standard and tachyon scalar fields and between their associated potentials, corresponding to the same background evolution. We show that, in general, the duality is broken at a perturbative level, when deviations from a homogeneous and isotropic background are taken into account. However, we find that for slow-rolling fields the duality is still preserved at a linear level. We illustrate our results with specific examples of cosmological relevance, where the correspondence between scalar and tachyon scalar field models can be calculated explicitly., Comment: 8 pages

The role of domain wall junctions in Carter's pentahedral model is investigated both analytically and numerically. We perform, for the first time, field theory simulations of such model with various initial conditions. We confirm that there are very specific realizations of Carter's model corresponding to square lattice configurations with X-type junctions which could be stable. However, we show that more realistic realizations, consistent with causality constraints, do lead to a scaling domain wall network with Y-type junctions. We determine the network properties and discuss the corresponding cosmological implications, in particular for dark energy., Comment: 6 pages, 6 figures

This work deals with bifurcation and pattern changing in models described by two real scalar fields. We consider generic models with quartic potentials and show that the number of independent polynomial coefficients affecting the ratios between the various domain wall tensions can be reduced to 4 if the model has a superpotential. We then study specific one-parameter families of models and compute the wall tensions associated with both BPS and non-BPS sectors. We show how bifurcation can be associated to modification of the patterns of domain wall networks and illustrate this with some examples which may be relevant to describe realistic situations of current interest in high energy physics. In particular, we discuss a simple solution to the cosmological domain wall problem., Comment: 10 pages, 32 figures, published version

We use a combination of analytic tools and an extensive set of the largest and most accurate three-dimensional field theory numerical simulations to study the dynamics of domain wall networks with junctions. We build upon our previous work and consider a class of models which, in the limit of large number $N$ of coupled scalar fields, approaches the so-called `ideal' model (in terms of its potential to lead to network frustration). We consider values of $N$ between N=2 and N=20, and a range of cosmological epochs, and we also compare this class of models with other toy models used in the past. In all cases we find compelling evidence for a gradual approach to scaling, strongly supporting our no-frustration conjecture. We also discuss the various possible types of junctions (including cases where there is a hierarchy of them) and their roles in the dynamics of the network. Finally, we revise the Zel'dovich bound and provide an updated cosmological bound on the energy scale of this type of defect network: it must be lower than $10 {\rm keV}$., Comment: Submitted to Phys. Rev. D

We investigate the presence of defect structures in generalized models described by real scalar field in $(1,1)$ space-time dimensions. We work with two distinct generalizations, one in the form of a product of functions of the field and its derivative, and the other as a sum. We search for static solutions and study the corresponding linear stability on general grounds. We illustrate the results with several examples, where we find stable defect structures of modified profile. In particular, we show how the new defect solutions may give rise to evolutions not present in the standard scenario in higher spatial dimensions., Comment: RevTex, 10 pages, 2 figures; version to appear in EPJC

We describe the results of the largest and most accurate three-dimensional field theory simulations of domain wall networks with junctions. We consider a previously introduced class of models which, in the limit of large number $N$ of coupled scalar fields, approaches the so-called `ideal' model (in terms of its potential to lead to network frustration). We consider values of $N$ between N=2 and N=20. In all cases we find compelling evidence for a gradual approach to scaling, with the quantitative scaling parameters having only a mild dependence on $N$. These results strongly support our no-frustration conjecture., Comment: 4 pages, 2 figures

We study a number of domain wall forming models where various types of defect junctions can exist. These illustrate some of the mechanisms that will determine the evolution of defect networks with junctions. Understanding these mechanisms is vital for a proper assessment of a number of cosmological scenarios: we will focus on the issue of whether or not cosmological frustrated domain wall networks can exist at all, but our results are also relevant for the dynamics of cosmic (super)strings, where junctions are expected to be ubiquitous. We also define and discuss the properties that would make up the ideal model in terms of hypothetical frustrated wall networks, and provide an explicit construction for such a model. We carry out a number of numerical simulations of the evolution of these networks, analyze and contrast their results, and discuss their implications for our no-frustration conjecture., Comment: 13 pages, 64 extremely low resolution eps files (to comply with arXiv size limits). A version with better quality figures is available from the authors

We discuss necessary conditions for a network of cosmic domain walls to have a chance of providing the dark energy that might explain the recent acceleration of the universe. We derive a strong bound on the curvature of the walls, which shows that viable candidate networks must be fine-tuned and non-standard. We also discuss various requirements that any stable lattice of frustrated walls must obey. We conjecture that, even though one can build (by hand) lattices that would be stable, no such lattices will ever come out of realistic domain wall forming cosmological phase transitions. We provide some simple numerical simulations that illustrate our results and correct some misconceptions in the published literature, but a detailed numerical analysis is left for a companion paper., Comment: 9 pages, 8 figures

We introduce a new phenomenological one-scale model for the evolution of domain wall networks, and test it against high-resolution field theory numerical simulations. We argue that previous numerical estimates of wall velocities are inaccurate, and suggest a more accurate method of measurement. We show that the model provides an adequate approximation to the evolution of key parameters characterizing the evolution of the network. We use the model to study possible scaling solutions for domain wall networks, and discuss some of their cosmological consequences., Comment: 10 pages, submitted to Phys Rev D

We study the cosmological evolution of domain wall networks in two and three spatial dimensions in the radiation and matter eras using a large number of high-resolution field theory simulations with a large dynamical range. We investigate the dependence of the uncertainty in key parameters characterising the evolution of the network on the size, dynamical range and number of spatial dimensions of the simulations and show that the analytic prediction compares well with the simulation results. We find that there is ample evidence from the simulations of a slow approach of domain wall networks towards a linear scaling solution. However, while at early times the uncertainty in the value of the scaling exponent is small enough for deviations from the scaling solution to be measured, at late times the error bars are much larger and no strong deviations from the scaling solution are found., Comment: 11 pages, 16 figures

We consider our universe as a 3d domain wall embedded in a 5d dimensional Minkowski space-time. We address the problem of inflation and late time acceleration driven by bulk particles colliding with the 3d domain wall. The expansion of our universe is mainly related to these bulk particles. Since our universe tends to be permeated by a large number of isolated structures, as temperature diminishes with the expansion, we model our universe with a 3d domain wall with increasing internal structures. These structures could be unstable 2d domain walls evolving to fermi-balls which are candidates to cold dark matter. The momentum transfer of bulk particles colliding with the 3d domain wall is related to the reflection coefficient. We show a nontrivial dependence of the reflection coefficient with the number of internal dark matter structures inside the 3d domain wall. As the population of such structures increases the velocity of the domain wall expansion also increases. The expansion is exponential at early times and polynomial at late times. We connect this picture with string/M-theory by considering BPS 3d domain walls with structures which can appear through the bosonic sector of a five-dimensional supergravity theory., Comment: To appear in Phys. Rev. D, 16 pages, 3 eps figures, minor changes and references added

We have studied the cosmological evolution of domain wall networks in two, three and four spatial dimensions using high-resolution field theory simulations. The dynamical range and number of our simulations is larger than in previous works, but does not allow us to exclude previous hints of deviations to the naively expected scale-invariant evolution. These results therefore suggest that the approach of domain wall networks to linear scaling is a much slower process than that of cosmic strings, which has been previously characterized in detail., Comment: 7 pages, submitted to Phys Rev D

We study the simplest class of Bekenstein-type, varying $\alpha$ models, in which the two available free functions (potential and gauge kinetic function) are Taylor-expanded up to linear order. Any realistic model of this type reduces to a model in this class for a certain time interval around the present day. Nevertheless, we show that no such model is consistent with all existing observational results. We discuss possible implications of these findings, and in particular clarify the ambiguous statement (often found in the literature) that ``the Webb results are inconsistent with Oklo''., Comment: 7 pages, 4 figures