Primordial magnetic fields from preheating at the electroweak scale

Abstract

We analyze the generation of helical magnetic fields during preheating in a model of low-scale electroweak (EW) hybrid inflation. We show how the inhomogeneities in the Higgs field, resulting from tachyonic preheating after inflation, seed the magnetic fields in a way analogous to that predicted by Vachaspati and Cornwall in the context of the EW symmetry breaking. At this stage, the helical nature of the generated magnetic fields is linked to the non-trivial winding of the Higgs-field. We analyze non-perturbatively the evolution of these helical seeds through the highly non-linear stages of symmetry breaking (SB) and beyond. Electroweak SB occurs via the nucleation and growth of Higgs bubbles which squeeze the magnetic fields into string-like structures. The W -boson charge density clusters in lumps around the magnetic strings. After symmetry breaking, a detailed analysis of the magnetic field Fourier spectrum shows two well differentiated components: a UV radiation tail at a temperature T ∼ 0.23 m H , slowly growing with time, and an IR peak associated to the helical magnetic fields, which seems to follow inverse cascade. The system enters a regime in which we observe that both the amplitude (ρ B /ρ EW ∼ 10 −2 ) and the correlation length of the magnetic field grow linearly with time. During this stage of evolution we also observe a power-law growth in the helical susceptibility. These properties support the possibility that our scenario could provide the seeds eventually evolving into the microgauss fields observed today in galaxies and clusters of galaxies.

Nonperturbative dynamics of reheating after inflation: A review

“…transitions in the early universe, including reheating after inflation, provide possible mechanisms for helical magnetic field generation. 246,247 However, connecting the typical causal length scale (the size of the horizon) at the time of generation in the early universe to galactic and cluster scales in the contemporary universe poses serious challenges. Such primordial magnetic fields can also generate stochastic gravitational waves.…”

Evolution of primordial magnetic fields in mean-field approximation

“…In particular, inflation-produced magnetic fields usually exhibit a power-law spectrum when they re-enter the horizon. Also, most of the generating mechanisms after inflation [98][99][100][101][102][103][104][105][106][107][108][109][110][111][112] repose on microphysical processes acting only on small scales. Therefore, the structure of the resulting magnetic field appears as a set of uncorrelated (Gaussiandistributed) eddies, which implies a k 2 -like spectrum.…”

“…1 Moreover, models for generating helical magnetic fields in the early universe exist in the literature ( [97]. For generation mechanisms of primordial helical magnetic fields see, e.g., [98][99][100][101][102][103][104][105][106][107][108][109][110][111][112]). …”

Evolution of the baryon asymmetry through the electroweak crossover in the presence of a helical magnetic field

“…A helical PMF can arise, for example, from axion dynamics during inflation [7][8][9][10][11][12][13][14] (see also Refs. [15,16]). Due to interactions of the hypermagnetic field with the charged plasma, the hypermagnetic helicity slowly decays.…”