We study gravitational waves generated by the cosmological magnetic fields induced via bubble collisions during the electroweak (EW) and QCD phase transitions. The magnetic field generation mechanisms considered here are based on the use of the fundamental EW minimal supersymmetric (MSSM) and QCD Lagrangians. The gravitational waves spectrum is computed using a magnetohydrodynamic (MHD) turbulence model. We find that gravitational wave spectrum amplitude generated by the EW phase transition peaks at frequency approximately 1-2 mHz, and is of the order of 10 −20 − 10 −21 ; thus this signal is possibly detectable by Laser Interferometer Space Antenna (LISA). The gravitational waves generated during the QCD phase transition, however, are outside the LISA sensitivity bands. PACS numbers: 98.70.Vc,98.80.Cq

Building on earlier work, we develop an equation-of-motion method for calculating magnetic seed fields generated from currents arising from charged W ± fields in bubble collisions during a firstorder primordial electroweak phase transition allowed in some proposed extensions of the Standard Model. The novel feature of our work is that it takes into account, for the first time, the dynamics of the bubble walls in such collisions. We conclude that for bubbles with sufficiently thin surfaces the magnetic seed fields may be comparable to, or larger than, those found in earlier work. Thus, our results strengthen the conclusions of previous studies that cosmic magnetic fields observed today may originate from seeds created during the electroweak phase transition, and consequently that these fields may offer a clue relevant to extensions of the Standard Model.

Bubble collisions in cosmological phase transitions are explored, taking the non-abelian character of the gauge fields into account. Both the QCD and electroweak phase transitions are considered. Numerical solutions of the field equations in several limits are presented.

We present a theory of the generation of magnetic seed fields in bubble collisions during a firstorder electroweak phase transition (EWPT) possible for some choices of parameters in the minimal supersymmetric Standard Model. The theory extends earlier work and is formulated to assess the importance of surface dynamics in such collisions. We are led to linearized equations of motion with O(3) symmetry appropriate for examining collisions in which the Higgs field is relatively unperturbed from its mean value in the collision volume. Coherent evolution of the charged W fields within the bubbles is the main source of the em current for generating the seed fields, with fermions also contributing through the conductivity terms. We present numerical simulations within this formulation to quantify the role of the surface of the colliding bubbles, particularly the thickness of the surface, and to show how conclusions drawn from earlier work are modified. The main sensitivity arises such that the steeper the bubble surface the more enhanced the seed fields become. Consequently, the magnetic seed fields may be several times larger and smoother over the collision volume than found in earlier studies. Our work thus provides additional support to the supposition that magnetic fields produced during the EWPT in the early universe seed the galactic and extragalactic magnetic fields observed today.PACS numbers: 98.62. En,98.80.Cq,

We calculate the magnetic field generated during bubble collisions in a first-order electroweak phase transition that may occur for some choices of parameters in the minimal supersymmetric standard model. We derive equations of motion from the electroweak Lagrangian that couple the Higgs field and the gauge fields of the standard model sector. We show that for sufficiently gentle collisions, where the Higgs field is relatively unperturbed in the bubble overlap region, the equations of motion can be linearized so that in the absence of fermions the charged W fields are the source of the electromagnetic current for generating the seed fields. Solutions of the equations of motion for the charged gauge fields and Maxwell's equations for the magnetic field in O1; 2 space-time symmetry are expressed in closed form by applying boundary conditions at the time of collision. Our results indicate that the magnetic fields generated by charged W fields in the collision are comparable to those found in previous work. The magnetic fields so produced could seed galactic and extra-galactic magnetic fields observed today.