Generation Of Primordial Magnetic Fields Research Articles

Magnetogenesis in Non-Local Models during Inflation

The generation of magnetic fields during the inflation in an electromagnetic model with a non-local form factor in Maxwell’s action is studied. The equations of motion for the electromagnetic field are derived and solved. It is found that the conformal symmetry breaking due to the non-local form factor does not lead to the generation of magnetic fields during the inflation in the absence of an interaction with the inflaton field. If such a coupling takes place, then the presence of the form factor inhibits the generation of primordial magnetic fields compared to the case where the non-local form factor is absent.

Effective field theory of magnetogenesis identify necessary and sufficient conditions

At astrophysical and cosmological scales, there is a detectable amount of magnetic field. There are several probable origins for this observed magnetic field, including the possibility of its origin in the early Universe. There are several models for primordial magnetogenesis, and if the inflationary background is taken into account, broken conformal invariance is required to generate a sufficient amount of magnetic field. The breaking of conformal invariance is introduced either by new couplings between electromagnetic field and inflaton field or including higher derivative terms to the theory. As a step to unify these different approaches in the literature, we propose an Effective Field Theory (EFT) approach based on expansion about the Hubble parameter (H) and its derivatives, where EFT parameters describe the magnetogenesis scenario in the early Universe, and different choices of parameters correspond to different models.We explicitly show that the generation of primordial magnetic fields requires two necessary conditions — conformal invariance breaking and causal propagation. While broken conformal invariance is a common requirement for primordial magnetogenesis, for the first time, we show that causal propagation is also a necessary condition. We confirm this by considering a specific model of primordial magnetogenesis.

Generation of Primordial Magnetic Fields from QED and Higgs-like Domain Walls in Einstein–Cartan Gravity

Spacetime torsion is known to be highly suppressed at the end of inflation, which is called preheating. This result was recently shown in (EPJ C (2022)) in the frame of Einstein–Cartan–Brans–Dicke inflation. In this paper, it is shown that a torsionful magnetogenesis in QED effective Lagrangean drives a torsion damping in order to be subsequently amplified by the dynamo effect after the generation of these magnetic fields seeds. This damping on amplification would depend upon the so-called torsion chirality. Here, a cosmic factor gkK is present where K is the contortion vector and k is the wave vector which is connected to the inverse of magnetic coherence length. In a second example, we find Higgs inlationary fields in Einstein–Cartan gravity thick domain walls (DWs). Recently, a modified Einstein–Cartan gravity was given by Shaposhnikov et al. [PRL (2020)] to obtain Higgs-like inflatons as a portal to dark energy. In the case of thick DW, we assume that there is a torsion squared influence, since we are in the early universe where torsion is not so weak as in the late universe as shown by Paul and SenGupta [EPJ C (2019)] in a 5D brane-world. A static DW solution is obtained when the inflationary potential vanishes and Higgs potential is a helical function. Recently, in the absence of inflation, domain wall dynamos were obtained in Einstein–Cartan gravity (EC) where the spins of the nucleons were orthogonal to the wall.

Generation of magnetic fields near QCD Transition by collapsing Z(3) domains

In this work we investigate the possibility of generation of primordial magnetic field in the early universe near the QCD phase transition epoch via the collapse of Z(3) domains. The Z(3) domain walls arise in the deconfined phase of the QCD (above Tsim 200 MeV) and their collapse leads to a net quark concentration near the wall boundary due to non-trivial reflection of quarks. We look at the response of leptons to this quark excess and find that leptons do not cancel the electric charge concentration due to the quarks. The wall collapse and a net charge concentration can lead to the generation of vorticity and turbulence in the primordial plasma. We estimate the magnitude of the magnetic field generated and find that it can be quite large mathcal {O}(10^{15-18}mathrm {G}). The mechanism is independent of the order of the QCD phase transition.

Scalar-vector-tensor gravity theories

We construct the consistent ghost-free covariant scalar-vector-tensor gravity theories with second order equations of motion with derivative interactions. We impose locality, unitarity, Lorentz invariance and pseudo-Riemannian geometry as the fundamental terms. In the tensor sector we require diffeomorphism invariance, whereas we allow the vector sector to be gauge invariant or not. The resulting Lagrangians consist of new genuine couplings among these fields with at most two derivatives per field. They propagate five physical degrees of freedom in the gauge invariant case and six degrees of freedom if the gauge invariance is broken. In the corresponding limit of the free general functions in the Lagrangian, one recovers the generalized Proca theories. These scalar-vector-tensor theories will have important implications for cosmological and astrophysical applications, among which we mention the application to inflation and generation of primordial magnetic fields, new black hole and neutron star solutions, dark matter and dark energy.

Vector Galileon and inflationary magnetogenesis

Cosmological inflation provides the initial conditions for the structure formation. However, the origin of large-scale magnetic fields can not be addressed in this framework. The key issue for this long-standing problem is the conformal invariance of the electromagnetic (EM) field in 4-D. While many approaches have been proposed in the literature for breaking conformal invariance of the EM action, here, we provide a completely new way of looking at the modifications to the EM action and generation of primordial magnetic fields during inflation. We explicitly construct a higher derivative EM action that breaks conformal invariance by demanding three conditions—theory be described by vector potential Aμ and its derivatives, Gauge invariance be satisfied, and equations of motion be linear in second derivatives of vector potential. The unique feature of our model is that appreciable magnetic fields are generated at small wavelengths while tiny magnetic fields are generated at large wavelengths that are consistent with current observations.

Non-Riemannian geometry, Born–Infeld models and trace free gravitational equations

Non-Riemannian generalization of the standard Born–Infeld (BI) Lagrangian is introduced and analyzed from a theory of gravitation with dynamical torsion field. The field equations derived from the proposed action lead to a trace free gravitational equation (non-Riemannian analog to the trace free equation (TFE) from Finkelstein et al., 2001; Ellis et al., 2011; Ellis, 2014) and the field equations for the torsion respectively. In this theoretical context, the fundamental constants arise all from the same geometry through geometrical invariant quantities (as from the curvature R). New results involving generation of primordial magnetic fields and the link with leptogenesis and baryogenesis are presented and possible explanations given. The physically admissible matter fields can be introduced in the model via the torsion vector hμ. Such fields include some dark matter candidates such as axion, right neutrinos and Majorana and moreover, physical observables as vorticity can be included in the same way. From a new wormhole solution in a cosmological spacetime with torsion we also show that the primordial cosmic magnetic fields can originate from hμ with the axion field (that is contained in hμ) the responsible to control the dynamics and stability of the cosmic magnetic field but not the magnetogenesis itself. As we pointed out before (Cirilo-Lombardo, 2017), the analysis of Grand Unified Theories (GUT) in the context of this model indicates that the group manifold candidates are based in SO(10), SU(5) or some exceptional groups as E(6), E(7), etc.

Primordial magnetic fields in the f2FF model in large field inflation under de Sitter and power law expansion

AbstractWe use the f2FF model to study the generation of primordial magnetic fields (PMF) in the context of large field inflation (LFI), described by the potential, V ∼ Mϕp. We compute the magnetic and electric spectra for all possible values of the model parameters under de Sitter and power law expansion. We show that scale invariant PMF are not obtained in LFI to first order in the slow roll approximation, if we impose the constraint V (ϕ = 0) ∼ 0. Alternatively, if these constraints are relaxed, the scale invariant PMF can be generated. The associated electric field energy can fall below the energy density of inflation, ρInf for the ranges of comoving wavenumbers, k > 8 × 10–7 Mpc–1 and k > 4 × 10–6 Mpc–1 in de Sitter and power law (PL) expansion. Further, it can drop below ρInf on the ranges, e‐foldings N > 51, p < 1.66, p > 2.03, l0 > 3 × 105 MPl–1(Hi < 3.3 × 10–6 MPl), and M > 2.8 × 10–3 MPl. All of the above ranges fit with the observational constraints. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Generation of scale invariant magnetic fields in bouncing universes

We consider the generation of primordial magnetic fields in a class of bouncing models when the electromagnetic action is coupled non-minimally to a scalar field that, say, drives the background evolution. For scale factors that have the power law form at very early times and non-minimal couplings which are simple powers of the scale factor, one can easily show that scale invariant spectra for the magnetic field can arise before the bounce for certain values of the indices involved. It will be interesting to examine if these power spectra retain their shape after the bounce. However, analytical solutions for the Fourier modes of the electromagnetic vector potential across the bounce are difficult to obtain. In this work, with the help of a new time variable that we introduce, which we refer to as the e-\U0001d4a9-fold, we investigate these scenarios numerically. Imposing the initial conditions on the modes in the contracting phase, we numerically evolve the modes across the bounce and evaluate the spectra of the electric and magnetic fields at a suitable time after the bounce. As one could have intuitively expected, though the complete spectra depend on the details of the bounce, we find that, under the original conditions, scale invariant spectra of the magnetic fields do arise for wavenumbers much smaller than the scale associated with the bounce. We also show that magnetic fields which correspond to observed strengths today can be generated for specific values of the parameters. But, we find that, at the bounce, the backreaction due to the electromagnetic modes that have been generated can be significantly large calling into question the viability of the model. We briefly discuss the implications of our results.

Cosmological magnetic fields as string dynamo seeds and axion fields in torsioned spacetime

In this paper two examples of the generation cosmological magnetic fields (CMF) are given. The first is the string dynamo seed cosmological magnetic field estimated as Bseed∼10-24 Gauss from a static spin polarised cylinder in Einstein-Cartan-Maxwell spacetime. The string dynamo seeds from a static spin polarised cylinder is given by B∼σ2R2 where σ is the spin-torsion density while R is the string radius. The B-field value above is able to seed galactic dynamo. In the BBN the magnetic fields around 1012 Gauss give rise to a string radius as small as 1017lP where lP is the Planck length. The second is the CMF from axionic torsion field which is given by Bseed∼10-27 Gauss which is stronger than the primordial magnetic field BBICEP2∼10-30 Gauss from the BICEP2 recent experiment on primordial gravitational waves and cosmological inflation to axionic torsion. The interaction Lagrangean between axionic torsion scalar ϕ and magnetic fields used in this last example is given by f2(ϕ)FμνFμν. A similar lagrangean has been used by K. Bamba et al. [JCAP 10 (2012) 058] so generate magnetic fields without dynamo action. Since axionic torsion can be associated with axionic domain walls both examples discussed here could be consider as topological defects examples of the generation of primordial magnetic fields in universes endowed with spacetime torsion.

Cosmological magnetogenesis from extra-dimensional Gauss-Bonnet gravity

Generation of primordial magnetic fields during inflation typically requires the breaking of conformal invariance of the Electromagnetic action. In this paper this has been achieved naturally in a higher dimensional cosmological model with a Gauss-Bonnet term in the action. The evolution of the scale factor of the extra dimension (whose dynamics is influenced by the Gauss-Bonnet term) acts as the cause for the breaking of conformal invariance. Different cases have been investigated, each of which is characterized by the number of higher dimensions, the value of the Gauss-Bonnet parameter, and the cosmological constant. Many of the scenarios considered are highly constrained by the requirements that the cosmic evolution is stable, that the normal dimensions expand and that there is no back reaction due to growing electric fields. However there do exist scenarios which satisfy the above requirements and are well suited for magnetogenesis. In particular, a scenario where the number of extra dimensions $D=4$ and the cosmological constant is non-zero, turns out to be best suited for generating primordial magnetic fields. It is shown that for these values of parameters, a scale invariant magnetic field of the order of $10^{-10}-10^{-9}$ $G$ can be produced. Even in these most favorable scenarios, the higher dimensional space expands during inflation at the same rate as the normal dimension. Hence if a mechanism could freeze the evolution of the higher dimension, this seems to be a viable mechanism to produce acceptable primordial magnetic fields.

Lorentz symmetry violation and galactic magnetism

We analyze the generation of primordial magnetic fields during de Sitter inflation in a Lorentz-violating theory of Electrodynamics containing a Chern–Simons term which couples the photon to an external four-vector. We find that, for appropriate magnitude of the four-vector, the generated field is maximally helical and, through an inverse cascade caused by turbulence of primeval plasma, reaches at the time of protogalactic collapse an intensity and correlation length such as to directly explain galactic magnetism.

Varying electromagnetic coupling and primordial magnetic fields

We study the effect of variations of the electromagnetic coupling on the process of generation of primordial magnetic fields. We find that only through a significant growth of the electromagnetic coupling can minimum seed fields be produced. We also show that, if through some process in the early Universe the photon acquires a mass that leads, thanks to inflation, to the generation of primordial magnetic fields, then the influence of variations of the electromagnetic coupling amounts essentially to the results due to the photon effective mass alone.

Generation of primordial magnetic fields by α-effect driven by collective neutrino-plasma interaction

We suggest a new mechanism for generation of large-scale magnetic fields in the hot plasma of early universe which is based on the parity violation in weak interactions. The mechanism can result in a self-excitation of an (almost) uniform cosmological magnetic field.

Self-consistent estimates of magnetic fields from reheating

We investigate the generation of primordial magnetic fields from stochastic currents created by the cosmological transition from inflation to reheating. We consider N charged scalar fields coupled to the electromagnetic field in a curved background and derive self-consistent equations for the evolution of the two point functions of the fields, which in the large-N limit give a decoupled set for the scalar and the electromagnetic functions. The main contribution to the electric current comes from the infrared portion of the spectrum of created particles, and in this limit the damping of the magnetic field is not due to normal conductivity but to London currents in the scalar field. For a given set of the physical parameters of the problem, we solved this equation numerically and found that, due to the fact that the London currents are oscillating, the field actually grows exponentially during the time interval in which our large-N limit equations are valid. Although for the chosen parameters the induced field is weak, the present uncertainties on their actual values leave open the possibility for higher intensities.

Phase equilibration and magnetic field generation in U(1) bubble collisions

We present the results of lattice computations of collisions of two expanding bubbles of true vacuum in the Abelian Higgs model with a first-order phase transition. New time-dependent analytical solutions for the Abelian field strength and the phase of the complex field are derived from initial conditions inferred from linear superposition and are shown to be in excellent agreement with the numerical solutions especially for the case where the initial phase difference between the bubbles is small. With a step-function approximation for the initial phase of the complex field, solutions for the Abelian field strength and other gauge-invariant quantities are obtained in closed form. Possible extensions of the solution to the case of the electroweak phase transition and the generation of primordial magnetic fields are briefly discussed.

Nonequilibrium quantum plasmas in scalar QED: Photon production, magnetic and Debye masses, and conductivity

We study the generation of a nonequilibrium plasma in scalar QED with N-charged scalar fields in the cases (a) of a supercooled second order phase transition through spinodal instabilities and (b) of parametric amplification when the order parameter oscillates with large amplitude around the minimum of the potential. The focus is to study the nonequilibrium electromagnetic properties of the plasma, such as photon production, electric and magnetic screening and conductivity. A novel kinetic equation is introduced to compute photon production far away from equilibrium in the large N limit and lowest order in the electromagnetic coupling. During the early stages of the dynamics the photon density grows exponentially and asymptotically the frequency distribution becomes ${N}_{\mathrm{ph}}(\ensuremath{\omega})\ensuremath{\sim}\ensuremath{\alpha}{m}^{2}/[{\ensuremath{\lambda}}^{2}{\ensuremath{\omega}}^{3}]$ with $\ensuremath{\lambda}$ the scalar self-coupling and m the scalar mass. In the case of a phase transition, electric and magnetic fields are correlated on distances $\ensuremath{\xi}(t)\ensuremath{\sim}\sqrt{t/m}$ during the early stages of the evolution and the power spectrum is peaked at low momentum. This aspect is relevant for the generation of primordial magnetic fields in the early Universe and for photoproduction as a potential experimental signature of the chiral phase transition. Magnetic and Debye screening masses are defined out of equilibrium as generalizations of the equilibrium case. While the magnetic mass vanishes out of equilibrium in this Abelian model, we introduce an effective time and wave-number dependent magnetic mass that reveals the different processes that contribute to screening and their time scales. The Debye mass turns out to be ${m}_{\mathrm{Deb}}^{2}\ensuremath{\sim}\ensuremath{\alpha}{m}^{2}/\ensuremath{\lambda}$ for a supercooled phase transition while in the case of an oscillating order parameter an interpolating time dependent Debye mass grows as $\ensuremath{\alpha}\sqrt{\mathrm{mt}}/\ensuremath{\lambda}$ due to a non-linear resonance at low momentum in the charged particle distribution. It is shown how the transverse electric conductivity builds up during the formation of the nonequilibrium plasma. Its long wavelength limit reaches a value ${\ensuremath{\sigma}}_{k\ensuremath{\approx}0}\ensuremath{\sim}\ensuremath{\alpha}m/\ensuremath{\lambda}$ at the end of the stage of linear instabilities. It is shown that the electric conductivity stays finite for all k including $k=0$ for finite time. In the asymptotic regime it attains a form analogous to the equilibrium case but in terms of the nonequilibrium particle distribution functions.

Cosmological magnetic fields from gauge-mediated supersymmetry-breaking models

We study the generation of primordial magnetic fields, coherent over cosmologically interesting scales, by gravitational creation of charged scalar particles during the reheating period. We show that magnetic fields consistent with those detected by observation may be obtained if the particle mean life τ s is in the range 10 −14 s ≲ τ s ≲10 −7 s. We apply this mechanism to minimal gauge-mediated supersymmetry-breaking models, in the case in which the lightest stau τ ̃ 1 is the next-to-lightest supersymmetric particle. We show that, for a large range of phenomenologically acceptable values of the supersymmetry-breaking scale F , the generated primordial magnetic field can be strong enough to seed the galactic dynamo.

Anomalous global strings and primordial magnetic fields

We propose a new mechanism for the generation of primordial magnetic fields, making use of the magnetic fields which are induced by anomalous global strings which couple to electromagnetism via Wess-Zumino type interactions. This mechanism can be realized in QCD by utilizing pion strings, global vortices which appear in the linear sigma model which describes physics below the QCD confinement scale. During the chiral symmetry breaking phase transition, pion strings can be produced, thus leading to primordial magnetic fields. We calculate the magnitude and coherence length of these fields. They are seen to depend on the string dynamics. With optimistic assumptions, both the magnitude and coherence scale of the induced magnetic fields can be large enough to explain the seed magnetic fields of greater than $10^{-23}$ Gauss necessary to produce the observed galactic magnetic fields via the galactic dynamo mechanism.

Magnetic fields from phase transitions

The generation of primordial magnetic fields from cosmological phase transitions is discussed, paying particular attention to the electroweak transition and to the various definitions of the `average' field that have been put forward. It is emphasised that only the volume average has dynamical significance as a seed for galactic dynamos. On rather general grounds of causality and energy conservation, it is shown that, in the absence of MHD effects that transfer power in the magnetic field from small to large scales, processes occurring at the electroweak transition cannot generate fields stronger than $10^{-20}$ Gauss on a scale of 0.5 Mpc. However, it is implausible that this upper bound could ever be reached, as it would require all the energy in the Universe to be turned into a magnetic field coherent at the horizon scale. Non-linear MHD effects seem therefore to be necessary if the electroweak transition is to create a primordial seed field.