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A short pedagogical overview of cosmological perturbation theory, following the lectures given during the brazilian school of cosmology held in August 2012. Topics treated are: I. The background II. SVT decomposition and the gauge issue. III. The example of the tensor modes. IV. Density fluctuations, transfer function and power spectrum. V. Initial condition theory: quantum vacuum fluctuations., Comment: Lecture notes from the Mangaratiba cosmology school, August 2012. To appear in the proceedings (S. Perez Bergliaffa and M. Novello, Eds., 2013)

We derive and solve a Boltzmann equation governing the cosmological evolution of the number density of current carrying cosmic string loops, whose centrifugally supported equilibrium configurations are also referred to as vortons. The phase space is three-dimensional and consists of the time variable, the loop size, and a conserved quantum number. Our approach includes gravitational wave emission, a possibly finite lifetime for the vortons and works with any initial loop distribution and for any loop production function. We then show how our results generalize previous approaches on the vorton excess problem by tracking down the time evolution of the various sub-populations of current-carrying loops in a string network., Comment: 19 pages, 2 figures, uses jcappub. References added, matches published version

Following recent claims relative to the question of large anisotropy production in regular bouncing scenarios, we study the evolution of such anisotropies in a model where an Ekpyrotic phase of contraction is followed by domination of a Galileon-type Lagrangian which generates a non-singular bounce. We show that the anisotropies decrease during the phase of Ekpyrotic contraction (as expected) and that they can be constrained to remain small during the non-singular bounce phase (a non-trivial result). Specifically, we derive the e-folding number of the phase of Ekpyrotic contraction which leads to a present-day anisotropy in agreement with current observational bounds., Comment: 12 pages, 5 figures

According to cosmological inflation, the inhomogeneities in our universe are of quantum mechanical origin. This scenario is phenomenologically very appealing as it solves the puzzles of the standard hot big bang model and naturally explains why the spectrum of cosmological perturbations is almost scale invariant. It is also an ideal playground to discuss deep questions among which is the quantum measurement problem in a cosmological context. Although the large squeezing of the quantum state of the perturbations and the phenomenon of decoherence explain many aspects of the quantum to classical transition, it remains to understand how a specific outcome can be produced in the early universe, in the absence of any observer. The Continuous Spontaneous Localization (CSL) approach to quantum mechanics attempts to solve the quantum measurement question in a general context. In this framework, the wavefunction collapse is caused by adding new non linear and stochastic terms to the Schroedinger equation. In this paper, we apply this theory to inflation, which amounts to solving the CSL parametric oscillator case. We choose the wavefunction collapse to occur on an eigenstate of the Mukhanov-Sasaki variable and discuss the corresponding modified Schroedinger equation. Then, we compute the power spectrum of the perturbations and show that it acquires a universal shape with two branches, one which remains scale invariant and one with nS=4, a spectral index in obvious contradiction with the Cosmic Microwave Background (CMB) anisotropy observations. The requirement that the non-scale invariant part be outside the observational window puts stringent constraints on the parameter controlling the deviations from ordinary quantum mechanics... (Abridged)., Comment: References added, minor corrections, conclusions unchanged

We present the simplest possible model for a semi-local string defect in which a U(1) gauged subgroup of an otherwise global SU(2) is broken to produce local cosmic strings endowed with current-carrying properties. Restricting attention to type II vortices for which the non current-carrying state is unstable, we show that a condensate must form microscopically and macroscopically evolve towards a chiral configuration. It has been suggested that such configurations could potentially exist in a stable state, thereby inducing large cosmological consequences based on equilibrium angular momentum supported loop configurations (vortons). Here we show that the current itself induces a macroscopic (longitudinal) instability: we conclude that type II semi-local cosmic strings cannot form in a cosmological context., Comment: 11 pages, 5 figures

Two-stream instability requires, essentially, two things to operate: a relative flow between two fluids and some type of interaction between them. In this letter we provide the first demonstration that this mechanism may be active in a cosmological context. Building on a recently developed formalism for cosmological models with two, interpenetrating fluids with a relative flow between them, we show that two-stream instability may be triggered during the transition from one fluid domination to the other. We also demonstrate that the cosmological expansion eventually shuts down the instability by driving to zero the relativeflow and the coupling between the two fluids., Comment: 9 pages, 3 figures. Final version that is published

Our current understanding of the Universe depends on the interplay of several distinct "matter" components, which interact mainly through gravity, and electromagnetic radiation. The nature of the different components, and possible interactions, tends to be based on the notion of coupled perfect fluids (or scalar fields). This approach is somewhat naive, especially if one wants to be able to consider issues involving heat flow, dissipative mechanisms, or Bose-Einstein condensation of dark matter. We argue that a more natural starting point would be the multi-purpose variational relativistic multi-fluid system that has so far mainly been applied to neutron star astrophysics. As an illustration of the fundamental principles involved, we develop the formalism for determining the non-linear cosmological solutions to the Einstein equations for a general relativistic two-fluid model for a coupled system of matter (non-zero rest mass) and "radiation" (zero rest mass). The two fluids are allowed to interpenetrate and exhibit a relative flow with respect to each other, implying, in general, an anisotropic Universe. We use initial conditions such that the massless fluid flux dominates early on so that the situation is effectively that of a single fluid and one has the usual Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. We find that there is a Bianchi I transition epoch out of which the matter flux dominates. The situation is then effectively that of a single fluid and the spacetime evolves towards the FLRW form. Such a transition opens up the possibility of imprinting observable consequences at the specific scale corresponding to the transition time., Comment: 12 pages, 6 figures, version taking account of referee remarks

I discuss, through a few examples, how observational cosmology can provide insights on hypothetical fundamental physics phenomena or mechanisms, such as Grand Unified Theory, Superstring alternatives to the inflation paradigm, and inflation itself., Comment: 4 pages, 4 figures - Proceedings of the french meeting "Societe Francaise d'Astronomie et d'Astrophysique" (SF2A) help in Marseille (France) in June 2010

A nonabelian generalization of the neutral Witten current-carrying string model is discussed in which the bosonic current-carrier belongs to a two dimensional representation of SU(2). We find that the current-carrying solutions can be of three different kinds: either the current spans a U(1) subgroup, and in which case one is left with an abelian current-carrying string, or the three currents are all lightlike, travelling in the same direction (only left or right movers). The third, genuinely nonabelian situation, cannot be handled within a cylindrically symmetric framework, but can be shown to depend on all possible string Lorentz invariant quantities that can be constructed out of the phase gradients., Comment: 13 pages, 1 figure

We investigate bouncing solutions in the framework of the non-singular gravity model of Brandenberger, Mukhanov and Sornborger. We show that a spatially flat universe filled with ordinary matter undergoing a phase of contraction reaches a stage of minimal expansion factor before bouncing in a regular way to reach the expanding phase. The expansion can be connected to the usual radiation- and matter-dominated epochs before reaching a final expanding de Sitter phase. In general relativity (GR), a bounce can only take place provided that the spatial sections are positively curved, a fact that has been shown to translate into a constraint on the characteristic duration of the bounce. In our model, on the other hand, a bounce can occur also in the absence of spatial curvature, which means that the timescale for the bounce can be made arbitrarily short or long. The implication is that constraints on the bounce characteristic time obtained in GR rely heavily on the assumed theory of gravity. Although the model we investigate is fourth order in the derivatives of the metric (and therefore unstable vis-a-vis the perturbations), this generic bounce dynamics should extend to string-motivated non singular models which can accommodate a spatially flat bounce., Comment: 9 pages, 10 figures

We first examine the microstructure of a cosmic string endowed with two simple Abelian currents. This microstructure depends on two state parameters. We then provide the macroscopic description of such a string and show that it depends on an additional Lorentz-invariant state parameter that relates the two currents. We find that in most of the parameter space, the two-current string is essentially equivalent to the single current-carrying string, i.e., only one field condenses onto the defect. In the regions where two currents are present, we find that as far as stability is concerned, one can approximate the dynamics with good accuracy using an analytic model based on either a logarithmic (on the electric side, i.e., for timelike currents) or a rational (on the magnetic side, i.e., for spacelike currents) worldsheet Lagrangian., Comment: 25 pages, 9 figures

We propose a new cosmological paradigm in which our observed expanding phase is originated from an initially large contracting Universe that subsequently experienced a bounce. This category of models, being geodesically complete, is non-singular and horizon-free, and can be made to prevent any relevant scale to ever have been smaller than the Planck length. In this scenario, one can find new ways to solve the standard cosmological puzzles. One can also obtain scale invariant spectra for both scalar and tensor perturbations: this will be the case, for instance, if the contracting Universe is dust-dominated at the time at which large wavelength perturbations get larger than the curvature scale. We present a particular example based on a dust fluid classically contracting model, where a bounce occurs due to quantum effects, in which these features are explicit., Comment: 8 pages, no figure

We perform a detailed investigation of the simplest possible cosmological model in which a bounce can occur, namely that where the dynamics is led by a simple massive scalar field in a general self-interacting potential and a background spacetime with positively curved spatial sections. By means of a phase space analysis, we give the conditions under which an initially contracting phase can be followed by a bounce and an inflationary phase lasting long enough (i.e., at least 60-70 e-folds) to suppress spatial curvature in today's observable universe. We find that, quite generically, this realization requires some amount of fine-tuning of the initial conditions. We study the effect of this background evolution on scalar perturbations by propagating an initial power-law power spectrum through the contracting phase, the bounce and the inflationary phase. We find that it is drastically modified, both spectrally (k-mode mixing) and in amplitude. It also acquires, at leading order, an oscillatory component, which, once evolved through the radiation and matter dominated eras, happens to be compatible with the WMAP data., Comment: Updated references, improved figure resolution

By demanding that a bounce is nonsingular and that perturbations are well-behaved at all times, we narrow the scope of possible models with one degree of freedom that can describe a bounce in the absence of spatial curvature. We compute the general properties of the transfer matrix of perturbations through the bounce, and show that spectral distortions of the Bardeen potential $\Phi$ are generically produced only for the small wavelengths, although the spectrum of long wavelength curvature perturbations produced in a contracting phase gets propagated unaffected through such a bounce., Comment: Replaced with version accepted to JCAP

We show that a contracting universe which bounces due to quantum cosmological effects and connects to the hot big-bang expansion phase, can produce an almost scale invariant spectrum of perturbations provided the perturbations are produced during an almost matter dominated era in the contraction phase. This is achieved using Bohmian solutions of the canonical Wheeler-de Witt equation, thus treating both the background and the perturbations in a fully quantum manner. We find a very slightly blue spectrum ($n_{_\mathrm{S}}-1>0$). Taking into account the spectral index constraint as well as the CMB normalization measure yields an equation of state that should be less than $\omega\lesssim 8\times 10^{-4}$, implying $n_{_\mathrm{S}}-1 \sim \mathcal{O}(10^{-4})$, and that the characteristic size of the Universe at the bounce is $L_0 \sim 10^3 \ell_\mathrm{Planck}$, a region where one expects that the Wheeler-DeWitt equation should be valid without being spoiled by string or loop quantum gravity effects., Comment: 9 pages, 4 figures

We discuss the gravitational wave background produced by bouncing models based on a full quantum evolution of a universe filled with a perfect fluid. Using an ontological interpretation for the background wave function allows us to solve the mode equations for the tensorial perturbations, and we find the spectral index as a function of the fluid equation of state., Comment: 12 pages, 5 figures, to appear in Phys. Rev. D (2006)

In the description of the dynamics of tensor perturbations on a homogeneous and isotropic background cosmological model, it is well known that a simple Hamiltonian can be obtained if one assumes that the background metric satisfies Einstein classical field equations. This makes it possible to analyze the quantum evolution of the perturbations since their dynamics depends only on this classical background. In this paper, we show that this simple Hamiltonian can also be obtained from the Einstein-Hilbert lagrangian without making use of any assumption about the dynamics of the background metric. In particular, it can be used in situations where the background metric is also quantized, hence providing a substantial simplification over the direct approach originally developed by Halliwell and Hawking., Comment: 24 pages, JHEP format

In this web note, we reply to a recent paper, gr-qc/0404126, confirming a previous work of ours in which a cosmological bouncing phase was shown to have the ability of modifying the spectrum of primordial perturbations (PRD 68, 103517 2003), but challenging its physical conditions of validity. Explicitly, Ref. gr-qc/0404126, besides pretending our Taylor series expansion of the scale factor close to the bounce amounts to choosing a family of polynomial scale factors, also claims that the bounce affects the spectrum only if the mass scale of the scalar field driving the dynamics is of the order of the Planck mass. We show that these objections are either misleading or incorrect since the minimum size of the Universe a_0 (value of the scale factor at the bounce) is either not physically specified, as required in a closed Universe, or implicitly assumed to be the Planck mass. We calculate this mass and obtain that, unsurprisingly, for a reasonable value of a_0, i.e. much larger than the Planck length, the scalar field mass is smaller than the Planck mass., Comment: 2 pages, Reply to gr-qc/0404126

We elaborate further on the evolution properties of cosmological fluctuations through a bounce. We show this evolution to be describable either by ``transmission'' and ``reflection'' coefficients or by an effective unitary S-matrix. We also show that they behave in a time reversal invariant way. Therefore, earlier results are now interpreted in a different perspective and put on a firmer basis., Comment: 4 pages, 1 figure, to appear in PRD

Using the simplest model for a bouncing universe, namely that for which gravity is described by pure general relativity, the spatial sections are positively curved and the matter content is a single scalar field, we obtain the transition matrix relating cosmological perturbation modes between the contracting and expanding phases. We show that this case provides a specific example in which this relation explicitely depends on the perturbation scale whenever the null energy condition (NEC) is close to be violated., Comment: 3 pages, 1 figure, to appear in the Tenth Marcel Grossmann Proceedings

We exhibit a situation in which cosmological perturbations of astrophysical relevance propagating through a bounce are affected in a scale-dependent way. Involving only the evolution of a scalar field in a closed universe described by general relativity, the model is consistent with causality. Such a specific counter-example leads to the conclusion that imposing causality is not sufficient to determine the spectrum of perturbations after a bounce provided it is known before. We discuss consequences of this result for string motivated scenarios., Comment: 4 pages, 1 figure, ReVTeX, to appear in Phys. Rev. Lett

We clarify the properties of the behavior of classical cosmological perturbations when the Universe experiences a bounce. This is done in the simplest possible case for which gravity is described by general relativity and the matter content has a single component, namely a scalar field in a closed geometry. We show in particular that the spectrum of scalar perturbations can be affected by the bounce in a way that may depend on the wave number, even in the large scale limit. This may have important implications for string motivated models of the early Universe., Comment: 17 pages, 12 figures, LaTeX-ReVTeX format, version to match Phys. Rev. D

By studying some bouncing universe models dominated by a specific class of hydrodynamical fluids, we show that the primordial cosmological perturbations may propagate smoothly through a general relativistic bounce. We also find that the purely adiabatic modes, although almost always fruitfully investigated in all other contexts in cosmology, are meaningless in the bounce or null energy condition (NEC) violation cases since the entropy modes can never be neglected in these situations: the adiabatic modes exhibit a fake divergence that is compensated in the total Bardeen gravitational potential by inclusion of the entropy perturbations., Comment: 25 pages, no figure, LaTeX

We study a six-dimensional braneworld model with infinite warped extra dimensions in the case where the four-dimensional brane is described by a topological vortex of a U(1) symmetry-breaking Abelian Higgs model in presence of a negative cosmological constant. A detailed analysis of the microscopic parameters leading to a finite volume space-time in the extra dimensions is numerically performed. As previously shown, we find that a fine-tuning is required to avoid any kind of singularity on the brane. We then discuss the stability of the vortex by investigating the scalar part of the gauge-invariant perturbations around this fine-tuned configuration. It is found that the hyperstring forming Higgs and gauge fields, as well as the background metric warp factors, cannot be perturbed at all, whereas transverse modes can be considered stable. The warped space-time structure that is imposed around the vortex thus appears severely constrained and cannot generically support nonempty universe models. The genericness of our conclusions is discussed; this will shed some light on the possibility of describing our space-time as a general six-dimensional warped braneworld., Comment: 26 pages, 13 figures, uses RevTex, fine-tuning and stability analysis discussed in greater details. Matches published version

The possibility of obtaining singularity free cosmological solutions in four dimensional effective actions motivated by string theory is investigated. In these effective actions, in addition to the Einstein-Hilbert term, the dilatonic and the axionic fields are also considered as well as terms coming from the Ramond-Ramond sector. A radiation fluid is coupled to the field equations, which appears as a consequence of the Maxwellian terms in the Ramond-Ramond sector. Singularity free bouncing solutions in which the dilaton is finite and strictly positive are obtained for models with flat or negative curvature spatial sections when the dilatonic coupling constant is such that $\omega < - 3/2$, which may appear in the so called $F$ theory in 12 dimensions. These bouncing phases are smoothly connected to the radiation dominated expansion phase of the standard cosmological model, and the asymptotic pasts correspond to very large flat spacetimes., Comment: 10 pages, ReVTeX format, 2 figures, to appear in Phys. Rev. D (2003)

With the new cosmological data gathered over the last few years, the inflationary paradigm has seen its predictions largely unchallenged. A recent proposal, called the ekpyrotic scenario, was argued to be a viable competitor as it was claimed that the spectrum of primordial perturbations it produces is scale invariant. By investigating closely this scenario, we show that the corresponding spectrum depends explicitly on an arbitrary function of wavenumber and is therefore itself arbitrary. It can at will be set scale invariant. We conclude that the scenario is not predictive at this stage., Comment: 4 pages, no figure, uses moriond.sty, to appear in the proceeding of the Moriond cosmology meeting held at Les Arcs, France (March 16-23, 2002)

In the paper ``Density perturbations in the ekpyrotic scenario'', it is argued that the expected spectrum of primordial perturbations should be scale invariant in this scenario. Here we show that, contrary to what is claimed in that paper, the expected spectrum depends on an arbitrary choice of matching variable. As no underlying (microphysical) principle exists at the present time that could lift the arbitrariness, we conclude that the ekpyrotic scenario is not yet a predictive model., Comment: 4 pages, no figure, RevTeX, commenting on hep-th/0109050

We construct a simple non singular cosmological model in which the currently observed expansion phase was preceded by a contraction. This is achieved, in the framework of pure general relativity, by means of a radiation fluid and a free scalar field having negative energy. We calculate the power spectrum of the scalar perturbations that are produced in such a bouncing model and find that, under the assumption of initial vacuum state for the quantum field associated with the hydrodynamical perturbation, this leads to a spectral index n=-1. The matching conditions applying to this bouncing model are derived and shown to be different from those in the case of a sharp transition. We find that if our bounce transition can be smoothly connected to a slowly contracting phase, then the resulting power spectrum will be scale invariant., Comment: 11 pages, RevTeX 4, 8 figures, submitted to Phys. Rev. D

The dynamical evolution of superconducting cosmic string loops with specific equations of state describing timelike and spacelike currents is studied numerically. This analysis extends previous work in two directions: first it shows results coming from a fully three dimensional simulation (as opposed to the two dimensional case already studied), and it now includes fermionic as well as bosonic currents. We confirm that in the case of bosonic currents, shocks are formed in the magnetic regime and kinks in the electric regime. For a loop endowed with a fermionic current with zero-mode carriers, we show that only kinks form along the string worldsheet, therefore making these loops slightly more stable against charge carrier radiation, the likely outcome of either shocks or kinks. All these combined effects tend to reduce the number density of stable loops and contribute to ease the vorton excess problem. As a bonus, these effects also may provide new ways of producing high energy cosmic rays., Comment: 11 pages, RevTeX 4 format, 8 figures, submitted to PRD

By considering a simplified but exact model for realizing the ekpyrotic scenario, we clarify various assumptions that have been used in the literature. In particular, we discuss the new ekpyrotic prescription for passing the perturbations through the singularity which we show to provide a spectrum depending on a non physical normalization function. We also show that this prescription does not reproduce the exact result for a sharp transition. Then, more generally, we demonstrate that, in the only case where a bounce can be obtained in Einstein General Relativity without facing singularities and/or violation of the standard energy conditions, the bounce cannot be made arbitrarily short. This contrasts with the standard (inflationary) situation where the transition between two eras with different values of the equation of state can be considered as instantaneous. We then argue that the usually conserved quantities are not constant on a typical bounce time scale. Finally, we also examine the case of a test scalar field (or gravitational waves) where similar results are obtained. We conclude that the full dynamical equations of the underlying theory should be solved in a non singular case before any conclusion can be drawn., Comment: 17 pages, ReVTeX 4, 13 figures, minor corrections, conclusions unchanged

We consider a cosmological setting for which the currently expanding era is preceded by a contracting phase, that is, we assume the Universe experienced at least one bounce. We show that scalar hydrodynamic perturbations lead to a singular behavior of the Bardeen potential and/or its derivatives (i.e. the curvature) for whatever Universe model for which the last bounce epoch can be smoothly and causally joined to the radiation dominated era. Such a Universe would be filled with non-linear perturbations long before nucleosynthesis, and would thus be incompatible with observations. We therefore conclude that no observable bounce could possibly have taken place in the early universe if Einstein gravity together with hydrodynamical fluids is to describe its evolution, and hence, under these conditions, that the Universe has always expanded., Comment: 11 pages, LaTeX-ReVTeX, no figures, submitted to PRD

We investigate the nature of ordinary cosmic vortices in some scalar-tensor extensions of gravity. We find solutions for which the dilaton field condenses inside the vortex core. These solutions can be interpreted as raising the degeneracy between the eigenvalues of the effective stress-energy tensor, namely the energy per unit length U and the tension T, by picking a privileged spacelike or timelike coordinate direction; in the latter case, a phase frequency threshold occurs that is similar to what is found in ordinary neutral current-carrying cosmic strings. We find that the dilaton contribution for the equation of state, once averaged along the string worldsheet, vanishes, leading to an effective Nambu-Goto behavior of such a string network in cosmology, i.e. on very large scales. It is found also that on small scales, the energy per unit length and tension depend on the string internal coordinates in such a way as to permit the existence of centrifugally supported equilibrium configuration, also known as vortons, whose stability, depending on the very short distance (unknown) physics, can lead to catastrophic consequences on the evolution of the Universe., Comment: 10 pages, ReVTeX, 2 figures, minor typos corrected. This version to appear in Phys. Rev. D

If space is compact, then a traveller twin can leave Earth, travel back home without changing direction and find her sedentary twin older than herself. We show that the asymmetry between their spacetime trajectories lies in a topological invariant of their spatial geodesics, namely the homotopy class. This illustrates how the spacetime symmetry invariance group, although valid {\it locally}, is broken down {\it globally} as soon as some points of space are identified. As a consequence, any non--trivial space topology defines preferred inertial frames along which the proper time is longer than along any other one., Comment: 6 pages, latex, 3 figures

We consider a network of topological defects which can partly decay into neutrinos, photons, baryons, or Cold Dark Matter. We find that the degree-scale amplitude of the cosmic microwave background (CMB) anisotropies as well as the shape of the matter power spectrum can be considerably modified when such a decay is taken into account. We conclude that present predictions concerning structure formation by defects might be unreliable., Comment: 14 pages, accepted for publication in PRD

The effect of fermionic string conductivity by purely right (or purely left) moving ``zero modes'' is shown to be governed by a simple Lagrangian characterising a certain ``chiral'' (null current carrying) string model whose dynamical equations of motion turn out to be explicitly integrable in a flat spacetime background., Comment: 7 pages, 2 eps figures included, uses ReVTeX

The role played by a primordial magnetic field during the pre-recombination epoch is analysed through the cyclotron radiation (due to the free electrons) it might produce in the primordial plasma. We discuss the constraint implied by the measurement or lack thereof COBE on this primordial field., Comment: to appear in International Journal of Mod. Phys

The modifications of circular cosmic string loop dynamics due to the electromagnetic self-interaction are calculated and shown to reduce the available phase space for reaching classical vorton states, thereby decreasing their remnant abundance. Use is made of the duality between master-function and Lagrangian formalisms on an explicit model., Comment: 10 pp RevTeX and 6 eps figures

A simple model is exhibited in which the remnant density of charged vortons is used to provide candidates for explaining the observed ultra high energy cosmic rays (above $10^{20}$ eV). These vortons would be accelerated in active galaxies and propagated through intergalactic medium with negligible losses of energy. The expected number density of observable events is shown to be consistent with extrapolation of the observations. The spectrum is predicted to be spatially isotropic while its shape is that of an atomic excitation-ionisation, i.e. with a few peaks followed by a continuum; there is also an energy threshold below which no vorton is visible., Comment: ReVTeX, 10 pages including 2 eps figures

Earlier attempts to calculate the nonlinear dynamical evolution of Witten type superconducting vacuum vortex defects relied on the use of approximate conducting string models that were too simple to take proper account of the effect of current saturation. This effect is however allowed for adequately in a newly developed class of rather more complicated, though still conveniently analytic, conducting string models. These more realistic models have recently been employed by Larsen and Axenides for investigating the collapse of circular string loops in the case for which angular momentum is absent. The present work extends this investigation to the generic case of circular string loops for which angular momentum is present, so that there will be a centrifugal potential barrier. This barrier will prevent collapse unless the initial conditions are such that the relevant current saturation limit is attained, in which case the string description of the vortex defect will break down, so that its subsequent fate is hard to foresee. On the other hand if saturation is avoided one would expect that the loop will eventually radiate away its excess energy and settle down into a vorton type equilibrium state., Comment: 15 pp RevTeX plus 6 PostScript figures

The topology of space is usually assumed simply connected, but could be multi-connected. We review in the latter case the possibility that topological defects arising at high energy phase transitions might still be present and find that either they are very unlikely to form at all, or space is effectively simply connected on scales up to the horizon size., Comment: LaTeX-REVTeX, 5 pages and 2 figures uuencoded, submitted to Phys. Rev. Lett

A synthesis of previous work done on the microscopic structure of cosmic strings in realistic models is made and reveals that strings are expected to be not only superconducting in the sense of Witten, but also generically current-carrying, either at the GUT scale or at the electroweak scale. This applies to any GUT string forming model leading to the standard electroweak theory as a low energy limit. The current consists of charged vector bosons. Cosmological consequences are briefly discussed., Comment: 5 pages, uses LaTeX-ReVTeX, no figures

Domain walls, arising from the spontaneous breaking of a discrete symmetry, can be coupled to charge carriers. In much the same way as the Witten model for superconducting cosmic string, an investigation is made here in the case of $U(1)\times Z_2 \to U(1)$, where a bosonic charge carrier is directly coupled to the wall-forming Higgs field. All internal quantities, such as the energy per unit surface and the surface current, are calculated numerically to provide the first complete analysis of the internal structure of a surface current-carrying domain wall., Comment: 11 pages, LaTeX-ReVTeX v.3, 2 figures available upon request

A new cosmic string model specified by two independent mass parameters is introduced for the purpose of providing a realistic representation of the macroscopic dynamical behaviour of Witten type (superconducting) vortex defects of the vacuum. Unlike the self dual single mass parameter models previously used for this purpose, the new model successfully represents the effect of current saturation and the feature that wiggle propagation remains supersonic even in the weak current limit., Comment: 7 pages, LaTeX-RevTeX, no figures