arXiv subjects
Publications and source records attributed to T. W. B. Kibble.
A recent claim by Lieu et al that beam splitter intensity subtraction (or homodyne with one vacuum port) followed by high resolution sampling can lead to detection of brightness of thermal light at the shot noise limit is reexamined here. We confirm the calculation of Zmuidzinas that the claim of Lieu et al was falsified by an incorrect assumption about the correlations in thermal noise.
In cosmological scenarios based on grand unification, string theory or braneworlds, many kinds of topological or non-topological defects, including monopoles and cosmic strings, are predicted to be formed in the early universe. Here we review specifically the physics of composite objects involving monopoles tied to strings. There is a wide variety of these, including for example "dumbbells" and "necklaces," depending on how many strings attach to each monopole and on the extent to which the various fluxes are confined to the strings. We also briefly survey the prospects for observing such structures, the existing observational limits, and potential evidence for a cosmological role.
In this talk, I recall the history of the development of the unified electroweak theory, incorporating the symmetry-breaking Higgs mechanism, as I saw it from my standpoint as a member of Abdus Salam's group at Imperial College. I start by describing the state of physics in the years after the Second World War, explain how the goal of a unified gauge theory of weak and electromagnetic interactions emerged, the obstacles encountered, in particular the Goldstone theorem, and how they were overcome, followed by a brief account of more recent history, culminating in the historic discovery of the Higgs boson in 2012.
The `missing baryons' of the near universe are believed to be principally in a partially ionized state. Although passing electromagnetic waves are dispersed by the plasma, the effect has hitherto not been utilized as a means of detection because it is generally believed that a successful observation requires the background source to be highly variable, \ie~the class of sources that could potentially deliver a verdict is limited. We argue in two stages that this condition is not necessary. First, by modeling the fluctuations on macroscopic scales as interference between wave packets we show that, in accordance with the ideas advanced by Einstein in 1917, both the behavior of photons as bosons (\ie~the intensity variance has contributions from Poisson and phase noise) and the van-Cittert-Zernike theorem are a consequence of wave-particle duality. Nevertheless, we then point out that in general the variance on some macroscopic timescale $τ$ consists of (a) a main contributing term $\propto 1/τ$, plus (b) a small negative term $\propto 1/τ^2$ due to the finite size of the wave packets. If the radiation passes through a dispersive medium, this size will be enlarged well beyond its vacuum minimum value of $Δt \approx 1/Δν$, leading to a more negative (b) term (while (a) remains unchanged) and hence a suppression of the variance w.r.t. the vacuum scenario. The phenomenon, which is typically at the few parts in 10$^5$ level, enables one to measure cosmological dispersion in principle. Signal-to-noise estimates, along with systematic issues and how to overcome them, will be presented.
When a second-order phase transition is crossed at fine rate, the evolution of the system stops being adiabatic as a result of the critical slowing down in the neighborhood of the critical point. In systems with a topologically nontrivial vacuum manifold, disparate local choices of the ground state lead to the formation of topological defects. The universality class of the transition imprints a signature on the resulting density of topological defects: It obeys a power law in the quench rate, with an exponent dictated by a combination of the critical exponents of the transition. In inhomogeneous systems the situation is more complicated, as the spontaneous symmetry breaking competes with bias caused by the influence of the nearby regions that already chose the new vacuum. As a result, the choice of the broken symmetry vacuum may be inherited from the neighboring regions that have already entered the new phase. This competition between the inherited and spontaneous symmetry breaking enhances the role of causality, as the defect formation is restricted to a fraction of the system where the front velocity surpasses the relevant sound velocity and phase transition remains effectively homogeneous. As a consequence, the overall number of topological defects can be substantially suppressed. When the fraction of the system is small, the resulting total number of defects is still given by a power law related to the universality class of the transition, but exhibits a more pronounced dependence on the quench rate. This enhanced dependence complicates the analysis but may also facilitate experimental test of defect formation theories.
In some versions of the theory of inflation, it is assumed that before inflation began the universe was in a Friedmann-Robertson-Walker (FRW) stage, with the energy density dominated by massless particles. The origin of the nearly scale-invariant density perturbations is quantum fluctuations in the inflaton field. Here we point out that under those conditions there would necessarily also be large thermally induced density perturbations. It is asserted that inflation would smooth out any pre-existing perturbations. But that argument relies on linear perturbation theory of the scalar modes, which would be rendered invalid because of the non-negligibility of the vector and tensor modes when the perturbation in the total density becomes large. Under those circumstances the original proof that inflation would have the desired smoothing effect no longer applies, {\it i.e.} for the theory to be robust an alternative (and hitherto unavailable) demonstration of the smoothing that takes account of these non-linear terms is necessary.
Using the chiral representation for spinors we present a particularly transparent way to generate the most general spinor dynamics in a theory where gravity is ruled by the Einstein-Cartan-Holst action. In such theories torsion need not vanish, but it can be re-interpreted as a 4-fermion self-interaction within a torsion-free theory. The self-interaction may or may not break parity invariance, and may contribute positively or negatively to the energy density, depending on the couplings considered. We then examine cosmological models ruled by a spinorial field within this theory. We find that while there are cases for which no significant cosmological novelties emerge, the self-interaction can also turn a mass potential into an upside-down Mexican hat potential. Then, as a general rule, the model leads to cosmologies with a bounce, for which there is a maximal energy density, and where the cosmic singularity has been removed. These solutions are stable, and range from the very simple to the very complex.
Cosmic strings are predicted by many field-theory models, and may have been formed at a symmetry-breaking transition early in the history of the universe, such as that associated with grand unification. They could have important cosmological effects. Scenarios suggested by fundamental string theory or M-theory, in particular the popular idea of brane inflation, also strongly suggest the appearance of similar structures. Here we review the reasons for postulating the existence of cosmic strings or superstrings, the various possible ways in which they might be detected observationally, and the special features that might discriminate between ordinary cosmic strings and superstrings.
We discuss some hitherto puzzling features of the small-scale structure of cosmic strings. We argue that kinks play a key role, and that an important quantity to study is their sharpness distribution. In particular we suggest that for very small scales the two-point correlation function of the string tangent vector varies linearly with the separation and not as a fractional power, as proposed by Polchinski and Rocha [Phys. Rev. D 74, 083504 (2006)]. However, our results are consistent with theirs, because the range of scales to which this linearity applies shrinks as evolution proceeds.
We suggest here a mechanism for the seeding of the primordial density fluctuations. We point out that a process like reheating at the end of inflation will inevitably generate perturbations, even on superhorizon scales, by the local diffusion of energy. Provided that the reheating temperature is of order the GUT scale, the density contrast $δ_R$ for spheres of radius $R$ will be of order $10^{-5}$ at horizon entry, consistent with the values measured by \texttt{WMAP}. If this were a purely classical process, $δ_R^2$ would fall as $1/R^4$ beyond the horizon, and the resulting primordial density power spectrum would be $P(k) \propto k^n$ with $n=4$. However, as shown by Gabrielli et al, a quantum diffusion process can generate a power spectrum with any index in the range $0 1$). Thus, the two characteristic parameters that determine the appearance of present day structures could be natural consequences of this mechanism. These are in any case the minimum density variations that must have formed if the universe was rapidly heated to GUT temperatures by the decay of a `false vacuum'. There is then no \emph{a priori} necessity to postulate additional (and fine tuned) quantum fluctuations in the `false vacuum', nor a pre-inflationary period. Given also the very stringent pre-conditions required to trigger a satisfactory period of inflation, altogether it seems at least as natural to assume that the universe began in a flat and homogeneously expanding phase.
We study the formation of monopoles and strings in a model where SU(3) is spontaneously broken to U(2)=[SU(2)\times U(1)]/\ZZ_2, and then to U(1). The first symmetry breaking generates monopoles with both SU(2) and U(1) charges since the vacuum manifold is \CC P^2. To study the formation of these monopoles, we explicitly describe an algorithm to detect topologically non-trivial mappings on \CC P^2. The second symmetry breaking creates \ZZ_2 strings linking either monopole-monopole pairs or monopole-antimonopole pairs. When the strings pull the monopoles together they may create stable monopoles of charge 2 or else annihilate. We determine the length distribution of strings and the fraction of monopoles that will survive after the second symmetry breaking. Possible implications for topological defects produced from the spontaneous breaking of even larger symmetry groups, as in Grand Unified models, are discussed.
Superstring theory predicts the potential formation of string networks with bound states ending in junctions. Kinematic constraints for junction formation have been derived within the Nambu-Goto thin string approximation. Here we test these constraints numerically in the framework of the Abelian-Higgs model in the Type-I regime and report on good agreement with the analytical predictions. We also demonstrate that strings can effectively pass through each other when they meet at speeds slightly above the critical velocity permitting bound state formation. This is due to reconnection effects that are beyond the scope of the Nambu-Goto approximation.
We study the formation of three-string junctions between (p,q)-cosmic superstrings, and collisions between such strings and show that kinematic constraints analogous to those found previously for collisions of Nambu-Goto strings apply here too, with suitable modifications to take account of the additional requirements of flux conservation. We examine in detail several examples involving collisions between strings with low values of p and q, and also examine the rates of growth or shrinkage of strings at a junction. Finally, we briefly discuss the formation of junctions for strings in a warped space, specifically with a Klebanov-Strassler throat, and show that similar constraints still apply with changes to the parameters taking account of the warping and the background flux.
We consider the constraints on string networks with junctions in which the strings may all be different, as may be found for example in a network of $(p,q)$ cosmic superstrings. We concentrate on three aspects of junction dynamics. First we consider the propagation of small amplitude waves across a static three-string junction. Then, generalizing our earlier work, we determine the kinematic constraints on two colliding strings with different tensions. As before, the important conclusion is that strings do not always reconnect with a third string; they can pass straight through one another (or in the case of non-abelian strings become stuck in an X configuration), the constraint depending on the angle at which the strings meet, on their relative velocity, and on the ratios of the string tensions. For example, if the two colliding strings have equal tensions, then for ultra-relativistic initial velocities they pass through one another. However, if their tensions are sufficiently different they can reconnect. Finally, we consider the global properties of junctions and strings in a network. Assuming that, in a network, the incoming waves at a junction are independently randomly distributed, we determine the r.m.s. velocities of strings and calculate the average speed at which a junction moves along each of the three strings from which it is formed. Our findings suggest that junction dynamics may be such as to preferentially remove the heavy strings from the network leaving a network of predominantly light strings. Furthermore the r.m.s. velocity of strings in a network with junctions is smaller than 1/\sqrt{2}, the result for conventional Nambu-Goto strings without junctions in Minkowski spacetime.
We study the dynamics of Nambu--Goto strings with junctions at which three strings meet. In particular, we exhibit one simple exact solution and examine the process of intercommuting of two straight strings, in which they exchange partners but become joined by a third string. We show that there are important kinematical constraints on this process. The exchange cannot occur if the strings meet with very large relative velocity. This may have important implications for the evolution of cosmic superstring networks and non-abelian string networks.
The aim of this paper is to re-examine the question of the average magnification in a universe with some inhomogeneously distributed matter. We present an analytic proof, valid under rather general conditions, including clumps of any shape and size, and strong lensing, that so long as the clumps are uncorrelated the average \emph{reciprocal} magnification (in one of several possible senses) is precisely the same as in a homogeneous universe with equal mean density. From this result, we also show that a similar statement can be made about one definition of average \emph{direct} magnification. We discuss, in the context of observations of discrete and extended sources, the physical significance of the various different measures of magnification and the circumstances in which they are appropriate.
Cosmic strings are linear concentrations of energy that may be formed at phase transitions in the very early universe. At one time they were thought to provide a possible origin for the density inhomogeneities from which galaxies eventually develop, though this idea has been ruled out, primarily by observations of the cosmic microwave background (CMB). Fundamental strings are the supposed building blocks of all matter in superstring theory or its modern version, M-theory. These two concepts were originally very far apart, but recent developments have brought them closer. The `brane-world' scenario in particular suggests the existence of macroscopic fundamental strings that could well play a role very similar to that of cosmic strings. In this paper, we outline these new developments, and also analyze recent observational evidence, and prospects for the future.
There are two main reasons for the recent renewal of interest in cosmic strings: Fundamental string-theory models suggest their existence; and there are at least two tentative observations of their possible effects. In this talk, I review their current status in the light of these two factors.