Massimo Giovannini

Warped compactification on Abelian vortex in six dimensions

We consider the possibility of localizing gravity on a Nielsen-Olesen vortex in the context of the Abelian Higgs model. The vortex lives in a six-dimensional space-time with negative bulk cosmological constant. In this model we find a region of the parameter space leading, simultaneously, to warped compactification and to regular space-time geometry. A thin defect limit is studied. Regular solutions describing warped compactifications in the case of higher winding number are also presented.

Gauge-invariant fluctuations of scalar branes

A generalization of the Bardeen formalism to the case of warped geometries is presented. The system determining the gauge-invariant fluctuations of the metric induced by the scalar fluctuations of the brane is reduced to a set of Schrodinger-like equations for the Bardeen potentials and for the canonical normal modes of the scalar-tensor action. Scalar, vector and tensor modes of the geometry are classified according to four-dimensional Lorentz transformations. While the tensor modes of the geometry live on the brane determining the corrections to Newton law, the scalar and vector fluctuations exhibit non-normalizable zero modes and are, consequently, not localized on the brane. The spectrum of the massive modes of the fluctuations is analyzed using supersymmetric quantum mechanics.

Primordial magnetic fields from inflation

The hot plasma above the electroweak scale contains (hyper) charged scalar particles which are coupled to Abelian gauge fields. Scalars may interact with gravity in a non-conformally invariant way and thus their fluctuations can be amplified during inflation. These fluctuations lead to creation of electric currents and produce inhomogeneous distribution of charge density, resulting in the generation of cosmological magnetic fields. We address the question whether these fields can be coherent at large scales so that they may seed the galactic magnetic fields. Depending upon the mass of the charged scalar and upon various cosmological (critical fraction of energy density in matter, Hubble constant) and particle physics parameters we found that the magnetic fields generated in this way are much larger than vacuum fluctuations. However, their amplitude on cosmological distances is found to be too small for seeding the galactic magnetic fields.

Localization of metric fluctuations on scalar branes

The localization of metric fluctuations on scalar brane configurations breaking spontaneously five-dimensional Poincare invariance is discussed. Assuming that the four-dimensional Planck mass is finite and that the geometry is regular, it is demonstrated that the vector and scalar fluctuations of the metric are not localized on the brane.

Thick branes and Gauss-Bonnet self-interactions

Thick branes obtained from a bulk action containing Gauss-Bonnet self-interactions are analyzed in light of the localization properties of the various modes of the geometry. The entangled system describing the localization of the tensor, vector, and scalar fluctuation is decoupled in terms of variables invariant for infinitesimal coordinate transformations. The dynamics of the various zero modes is discussed and solved in general terms. Provided the four-dimensional Planck mass is finite and provided the geometry is everywhere regular, it is shown that the vector and scalar zero modes are not localized. The tensor zero mode is localized leading to four-dimensional gravity. The general formalism is illustrated through specific analytical examples.

On the variation of the gauge couplings during inflation

It is shown that the evolution of the (Abelian) gauge coupling during an inflationary phase of de Sitter type drives the growth of the two-point function of the magnetic inhomogeneities. After examining the constraints on the variation of the gauge coupling arising in a standard model of inflationary and post-inflationary evolution, magnetohydrodynamical equations are generalized to the case of time evolving gauge coupling. It is argued that large scale magnetic fields can be copiously generated. Other possible implications of the model are outlined.

Magnetogenesis and the dynamics of internal dimensions

The dynamical evolution of internal spacelike dimensions breaks the invariance of Maxwells equations under Weyl rescaling of the (conformally flat) four-dimensional metric. Depending upon the number and upon the dynamics of internal dimensions large scale magnetic fields can be created. The requirements coming from magnetogenesis together with the other cosmological constraints are examined under the assumption that the internal dimensions either grow or shrink (in conformal time) prior to a radiation-dominated epoch. If the internal dimensions are growing, the magnitude of the generated magnetic fields can seed the galactic dynamo mechanism.

Gauge field localization on Abelian vortices in six-dimensions

The vector and tensor fluctuations of vortices localizing gravity in the context of the six-dimensional Abelian Higgs model are studied. These string-like solutions break spontaneously six-dimensional Poincare invariance leading to a finite four-dimensional Planck mass and to a regular geometry both in the bulk and on the core of the vortex. While the tensor modes of the metric are decoupled and exhibit a normalizable zero mode, the vector fluctuations, present in the gauge sector of the theory, are naturally coupled to the graviphoton fields associated with the vector perturbations of the warped geometry. Using the invariance under infinitesimal diffeomorphisms, it is found that the zero modes of the graviphoton fields are never localized. On the contrary,the fluctuations of the Abelian gauge field itself admit a normalizable zero mode.

Zero modes of six-dimensional Abelian vortices

We analyse the fluctuations of Nielsen–Olesen vortices arising in the six-dimensional Abelian–Higgs model. The regular geometry generated by the defect breaks spontaneously six-dimensional Poincare symmetry leading to a warped spacetime with finite four-dimensional Planck mass. As a consequence, the zero mode of the spin-two fluctuations of the geometry is always localized, but the graviphoton fields, corresponding to spin-one metric fluctuations, give rise to zero modes which are not localized either because of their behaviour at infinity or because of their behaviour near the core of the vortex. A similar situation occurs for spin zero fluctuations. Gauge field fluctuations exhibit a localized zero mode.

Scalar normal modes of higher-dimensional gravitating kinks

The scalar normal modes of higher-dimensional gravitating kink solutions are derived. By perturbing to second order the gravity and matter parts of the action in the background of a five-dimensional kink, the effective Lagrangian of the scalar fluctuations is derived and diagonalized in terms of a single degree of freedom which is invariant under infinitesimal diffeomorphisms. The spectrum of the normal modes is discussed and applied to the analysis of short distance corrections to Newtons law.