Magnetic monopoles and vortices in the standard model of electroweak interactions

These lectures start with an elementary introduction to the subject of magnetic monopoles which should be accesible from any physics background. In the Weinberg-Salam model of electroweak interactions, magnetic monopoles appear at the ends of a type of non-topological vortices called electroweak strings. These will also be discussed, as well as recent simulations of their formation during a phase transition which indicate that, in the (unphysical) range of parameters in which the strings are classically stable, they can form with a density comparable to topological vortices.Comment: 19 pages, Les Houches lectures, NATO-ASI on Topological defects and the non-equilibrium dynamics of symmetry breaking phase transitions, Feb. 9

Relating black holes in two and three dimensions

The three dimensional black hole solutions of Ba\~nados, Teitelboim and Zanelli (BTZ) are dimensionally reduced in various different ways. Solutions are obtained to the Jackiw-Teitelboim theory of two dimensional gravity for spinless BTZ black holes, and to a simple extension with a non-zero dilaton potential for black holes of fixed spin. Similar reductions are given for charged black holes. The resulting two dimensional solutions are themselves black holes, and are appropriate for investigating exact ``S-wave'' scattering in the BTZ metrics. Using a different dimensional reduction to the string inspired model of two dimensional gravity, the BTZ solutions are related to the familiar two dimensional black hole and the linear dilaton vacuum.Comment: 12 pages, CTP #2181, January 199

The string swampland constraints require multi-field inflation

An important unsolved problem that affects practically all attempts to connect string theory to cosmology and phenomenology is how to distinguish effective field theories belonging to the string landscape from those that are not consistent with a quantum theory of gravity at high energies (the "string swampland"). It was recently proposed that potentials of the string landscape must satisfy at least two conditions, the "swampland criteria", that severely restrict the types of cosmological dynamics they can sustain. The first criterion states that the (multi-field) effective field theory description is only valid over a field displacement $\Delta \phi \leq \Delta \sim \mathcal O(1)$ (in units where the Planck mass is 1), measured as a distance in the target space geometry. A second, more recent, criterion asserts that, whenever the potential $V$ is positive, its slope must be bounded from below, and suggests $|\nabla V| / V \geq c \sim \mathcal O(1)$. A recent analysis concluded that these two conditions taken together practically rule out slow-roll models of inflation. In this note we show that the two conditions rule out inflationary backgrounds that follow geodesic trajectories in field space, but not those following curved, non-geodesic, trajectories (which are parametrized by a non-vanishing bending rate $\Omega$ of the multi-field trajectory). We derive a universal lower bound on $\Omega$ (relative to the Hubble parameter $H$) as a function of $\Delta, c$ and the number of efolds $N_e$, assumed to be at least of order 60. If later studies confirm $c$ and $\Delta$ to be strictly $\mathcal O(1)$, the bound implies strong turns with $\Omega / H \geq 3 N_e \sim 180$. Slow-roll inflation in the landscape is not ruled out, but it is strongly multi-field.Comment: v1: 15 pages; v2: 16 pages, references added, improved discussions, version accepted for publication in JCA

Robust predictions for an oscillatory bispectrum in Planck 2015 data from transient reductions in the speed of sound of the inflaton

We update the search for features in the Cosmic Microwave Background (CMB) power spectrum due to transient reductions in the speed of sound, using Planck 2015 CMB temperature and polarisation data. We enlarge the parameter space to much higher oscillatory frequencies of the feature, and define a robust prior independent of the ansatz for the reduction, guaranteed to reproduce the assumptions of the theoretical model and exhaustive in the regime in which the feature is easily distinguishable from the baseline cosmology. We find a fit to the $\ell\approx20$--$40$ minus/plus structure in Planck TT power spectrum, as well as features spanning along the higher $\ell$'s ($\ell\approx100$--$1500$). For the last ones, we compute the correlated features that we expect to find in the CMB bispectrum, and asses their signal-to-noise and correlation to the ISW-lensing secondary bispectrum. We compare our findings to the shape-agnostic oscillatory template tested in Planck 2015, and we comment on some tantalising coincidences with some of the traits described in Planck's 2015 bispectrum data.Comment: 19 pages - matches published versio

The two-field regime of natural inflation

The simplest two-field completion of natural inflation has a regime in which both fields are active and in which its predictions are within the Planck 1-$\sigma$ confidence contour. We show this for the original model of natural inflation, in which inflation is achieved through the explicit breaking of a U(1) symmetry. We consider the case in which the mass coming from explicit breaking of this symmetry is comparable to that from spontaneous breaking, which we show is consistent with a hierarchy between the corresponding energy scales. While both masses are comparable when the observable modes left the horizon, the mass hierarchy is restored in the last e-foldings of inflation, rendering the predictions consistent with the isocurvature bounds. For completeness, we also study the predictions for the case in which there is a large hierarchy of masses and an initial period of inflation driven by the (heavy) radial field.Comment: 18 pages, 9 figure

Exotic composites: the decay of deficit angles in global-local monopoles

We study static, spherically symmetric, composite global-local monopoles with a direct interaction term between the two sectors in the regime where the interaction potential is large. At some critical coupling the global defect disappears and with it the deficit angle of the space-time. We find new solutions which represent local monopoles in an Anti-de-Sitter spacetime. In another parameter range the magnetic monopole, or even both, disappear. The decay of the magnetic monopole is accompanied by a dynamical transition from the higgsed phase to the gauge-symmetric phase. We comment on the applications to cosmology, topological inflation and braneworlds.Comment: 17 pages, 11 figures; Minor corrections, matches published versio

Cumulative effects in inflation with ultra-light entropy modes

In multi-field inflation one or more non-adiabatic modes may become light, potentially inducing large levels of isocurvature perturbations in the cosmic microwave background. If in addition these light modes are coupled to the adiabatic mode, they influence its evolution on super horizon scales. Here we consider the case in which a non-adiabatic mode becomes approximately massless ("ultralight") while still coupled to the adiabatic mode, a typical situation that arises with pseudo-Nambu-Goldstone bosons or moduli. This ultralight mode freezes on super-horizon scales and acts as a constant source for the curvature perturbation, making it grow linearly in time and effectively suppressing the isocurvature component. We identify a Stuckelberg-like emergent shift symmetry that underlies this behavior. As inflation lasts for many e-folds, the integrated effect of this source enhances the power spectrum of the adiabatic mode, while keeping the non-adiabatic spectrum approximately untouched. In this case, towards the end of inflation all the fluctuations, adiabatic and non-adiabatic, are dominated by a single degree of freedom.Comment: 27 pages, 1 figure; v2: improved discussions, version published in JCA

Helical Magnetic Fields from Sphaleron Decay and Baryogenesis

Many models of baryogenesis rely on anomalous particle physics processes to give baryon number violation. By numerically evolving the electroweak equations on a lattice, we show that baryogenesis in these models creates helical cosmic magnetic fields. After a transitory period, electroweak dynamics is found to conserve the Chern-Simons number and the total electromagnetic helicity. We argue that baryogenesis could lead to magnetic fields of nano-Gauss strength today on astrophysical length scales. In addition to being astrophysically relevant, such helical magnetic fields can provide an independent probe of baryogenesis and CP violation in particle physics.Comment: 4 pages, 1 figure. Added references, fixed typo