We study the formation of monopoles and strings in a model where SU (3) is spontaneously broken to U (2) = [SU (2) × U (1)]/Z2, and then to U (1). The first symmetry breaking generates monopoles with both SU (2) and U (1) charges since the vacuum manifold is CP 2 . To study the formation of these monopoles, we explicitly describe an algorithm to detect topologically non-trivial mappings on CP 2 . The second symmetry breaking creates Z2 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.

Helical magnetic fields are injected into the cosmic medium during cosmological baryogenesis and can potentially provide a useful probe of the early universe. We construct a model to study the injection process during a first order phase transition and to determine the power spectra of the injected magnetic field. By Monte Carlo simulations we evaluate the Fourier space symmetric and helical power spectra of the magnetic field at the time the phase transition completes. The spectra are peaked at the scale given by the inverse size of bubbles at percolation and with a comparable width. These injected magnetic fields set the initial conditions for further cosmological magnetohydrodynamical evolution.Our study of the universe relies on relics left-over from early cosmological epochs. The cosmic microwave background brings information from the epoch when atoms formed, the light elemental abundances from the epoch when nuclei formed. Similarly, the electroweak phase transition may mark the epoch when a net baryon number was generated, or when net lepton number was converted into net baryon number, and this coincides with the generation of magnetic fields. The present paper is based on the hypothesis that primordial magnetic fields will inform us of the epoch when a net amount of baryons first formed, the so-called epoch of "baryogenesis" [1,2].The question of whether a primordial magnetic field exists is often raised in connection with the magnetic fields observed in galaxies and clusters of galaxies with strength ∼ µG and kpc-Mpc coherence scale. There is considerable debate whether primordial fields are essential to the generation of galactic fields, and what properties of the primordial field are necessary to turn them into observed magnetic structures. The arguments involve the coherence and amplitude of observed magnetic fields, the efficiency of galactic dynamos, the turnover time scales associated with galactic dynamics, especially with the earliest known galaxies containing magnetic structures, astrophysical sources e.g. active galactic nuclei that may spew out magnetic fields, and the generation of large scale seed fields by the Biermann battery. We shall by-pass these issues since, in our view, a primordial magnetic field is of interest in itself, whether or not it is responsible for the observed magnetic fields in galaxies. If there are strongly motivated early universe scenarios, based on reasonably well-established particle physics, that lead to the generation of magnetic fields, they provide good reason to study and to look for these structures in cosmological data.The connection between baryon number production and primordial magnetic fields can be understood intuitively in the following way. Baryon number violation in the standard model of the electroweak interactions is made possible due to a quantum anomaly. As a physical process, baryon number is generated when many different particles come together to form an object called a "sphaleron" [3,4], which then decays into a final state with baryon number...

We construct the most general effective Lagrangian coupling gravity and electromagnetism up to mass dimension 6 by enumerating all possible non-minimal coupling terms respecting both diffeomorphism and gauge invariance. In all, there are only two unique terms after field re-definitions; one is known to arise from loop effects in QED while the other is a parity violating term which may be generated by weak interactions within the standard model of particle physics. We show that neither the cosmological propagation of light nor, contrary to earlier claims, solar system tests of General Relativity are useful probes of these terms. These non-minimal couplings of gravity and electromagnetism may remain a mystery for the foreseeable future.