Electroweak Baryogenesis and Primordial Hypermagnetic Fields

Abstract

The origin of the matter-antimatter asymmetry of the universe remains one of the outstanding questions yet to be answered by modern cosmology and also one of only a handful of problems where the need of a larger number of degrees of freedom than those contained in the standard model (SM) is better illustrated. An appealing scenario for the generation of baryon number is the electroweak phase transition that took place when the temperature of the universe was about 100 GeV. Though in the minimal version of the SM, and without considering the interaction of the SM particles with additional degrees of freedom, this scenario has been ruled out given the current bounds for the Higgs mass, this still remains an open possibility in supersymmetric extensions of the SM. In recent years it has also been realized that large scale magnetic fields could be of primordial origin. A natural question is what effect, if any, these fields could have played during the electroweak phase transition in connection to the generation of baryon number. Prior to the electroweak symmetry breaking, the magnetic modes able to propagate for large distances belonged to the U (1) group of hypercharge and hence receive the name of hypermagnetic fields. In this contribution, we summarize recent work aimed to explore the effects that these fields could have introduced during a first order electroweak phase transition. In particular, we show how these fields induce a CP asymmetric scattering of fermions off the true vacuum bubbles nucleated during the phase transition. The segregated axial charge acts as a seed for the generation of baryon number. We conclude by mentioning possible research venues to further explore the effects of large scale magnetic fields for the generation of the baryon asymmetry.

Effective electromagnetic lagrangian at finite temperature and density in the electroweak model

“…In vacuum the effective EM action S of the electroweak model at the one-loop level can be written as S = 4 (30) and the effective EM lagrangian is given by…”

“…Recently there has been much interest [24][25][26] in studying the finite temperature Casimir effect in higher dimensional space-time models with compactified extra dimensions, like the Randall-Sundrum models [27,28]. A literature search reveals that the effective lagrangian in a background magnetic field at finite temperature and density has been studied within the framework of QED [10][11][12]18], or within the framework of the electroweak model but prior to the breaking of the electroweak symmetry, when the magnetic fields that are present belong to the U(1) group of hypercharge and hence are called hypermagnetic fields [29][30][31]. The electroweak phase transition at finite temperature and in an external hypercharge magnetic field has been studied non-perturbatively using numerical techniques such as lattice Monte Carlo simulations [32], and perturbatively [33].…”

Warm inflation in presence of magnetic fields

“…Performing a weak field expansion in Eqs. (19) and (20) [51,52] it is possible to carry out the sum over Landau levels to write the scalar and fermion propagators as power series in eB, which up to order (eB) 2 read as…”

“…These phase transitions include the electroweak phase transition [16][17][18], with par-ticular emphasis on the baryogenesis process (See [19] for a review; see also [20]), or the supersymmetry phase transition [21]. The studies include also the effects of PMF on the cosmic background radiation (see e.g.…”

MSM Self-Energies at Finite Temperature in the Presence of Weak Magnetic Fields: Towards a Full Symmetry Restoration Study

“…In a recent work [7,8,9] the development of the EWPT in the MSM from the symmetric phase has been studied in the presence of a weak external hypermagnetic field up to the contribution of ring diagrams. The main result is that the presence of the field strengthens the first order nature of the phase transition.…”