History of electroweak symmetry breaking

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 Salams 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.

Cosmology with a spin

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.

Large pre-inflationary thermal density perturbations

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Cosmic Strings and Superstrings

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.

A natural origin of primordial density perturbations

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 $delta_R$ 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, $delta_R^2$ 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 $0<nleq 4$, including values close to the observed $n=1$ ($delta_R^2$ will then be $propto 1/R^{3+n}$ for $n<1$ and $1/R^4$ for $n>1$). 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.

Formation of Non-Abelian Monopoles Connected by Strings

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.

On the Collision of Cosmic Superstrings

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.