Hypermagnetic Fields Research Articles

Production of Relic Gravitational Waves and the Baryon Asymmetry of the Universe by Random Hypermagnetic Fields

Production of Relic Gravitational Waves and the Baryon Asymmetry of the Universe by Random Hypermagnetic Fields

The scaling of primordial gauge fields

The large-scale magnetic fields arising from the quantum mechanical fluctuations of the hypercharge are investigated when the evolution of the gauge coupling is combined with a sufficiently long inflationary stage. In this framework the travelling waves associated with the quantum mechanical initial conditions turn asymptotically into standing waves which are the gauge analog of the Sakharov oscillations. Even if the rate of dilution of the hypermagnetic and hyperelectric fields seems to be superficially smaller than expected from the covariant conservation of the energy-momentum tensor, the standard evolution for wavelengths larger than the Hubble radius fully accounts for this anomalous scaling which is anyway unable to increase the amplitude of the magnetic power spectra after symmetry breaking. An effective amplification of the gauge power spectra may instead occur when the post-inflationary expansion rate is slower than radiation. We stress that the modulations of the gauge power spectra freeze as soon as the relevant wavelengths reenter the Hubble radius and not at the end of inflation. After the Mpc scale crosses the comoving Hubble radius the scaling of the magnetic power spectrum follows from the dominance of the conductivity. From these two observations the late-time values of the magnetic power spectra are accurately computed in the case of a nearly scale-invariant slope and contrasted with the situation where the phases of Sakharov oscillations are not evaluated at horizon crossing but at the end of inflation, i.e. when all the wavelengths relevant for magnetogenesis are still larger than the comoving horizon.

Electroweak sphaleron in a magnetic field

Using lattice simulations we calculate the rate of baryon number violating processes, the sphaleron rate, in the Standard Model with an external (hyper)magnetic field for temperatures across the electroweak cross-over, focusing on the broken phase. Additionally, we compute the Higgs expectation value and the pseudocritical temperature. The electroweak cross-over shifts to lower temperatures with increasing external magnetic field, bringing the onset of the suppression of the baryon number violation with it. When the hypermagnetic field reaches the magitude $B_Y \approx 2 T^2$ the cross-over temperature is reduced from $160$ GeV to $145$ GeV. In the broken phase for small magnetic fields the rate behaves quadratically as a function of the magnetic flux. For stronger magnetic fields the rate reaches a linear regime which lasts until the field gets strong enough to restore the electroweak symmetry where the symmetric phase rate is reached.

Anisotropic gravitational waves induced by hypermagnetic fields during the electroweak phase transition epoch

We study the anisotropies of gravitational waves induced by weak hypermagnetic fields which are randomly distributed and oriented during the electroweak phase transition in the early universe. The theory setup of this study is the standard model plus a real singlet scalar field, which can produce the needed strongly first order electroweak phase transition. Then we investigate how the hypermagnetic fields can convert to magnetic fields and we compute the departure of energy difference between the symmetric phase and the broken phase when the magnetic fields are turned on. It is found that the presence of the hypermagnetic fields can increase the Euclidean action, thus can decrease nucleation temperature, which can lead to a supercool plasma. We point out that the hypermagnetic field can enhance the gravitational wave production from a first order electroweak phase transition and the inhomogeneity of primordial hypermagnetic field can lead to anisotropies of gravitational waves. By examining three well-motivated distribution of hypermagnetic fields, we calculate the corresponding angular power spectra of stochastic gravitational wave background and find they can be significantly larger than the contributions of the Sachs-Wolfe effects and integrated Sachs-Wolfe effects. Our results show that the anisotropies of gravitational wave could provide a novel probe to the primordial hypermagnetic field in the electroweak phase transition epoch.

Numerical study of the Schwinger effect in axion inflation

Previous studies demonstrate that the inflaton, when coupled to the hypercharge Chern-Simons density, can source an explosive production of helical hypermagnetic fields. Then, in the absence of fermion production, those fields have the capability of preheating the Universe after inflation and triggering a successful baryogenesis mechanism at the electroweak phase transition. In the presence of fermion production, however, we expect a strong damping of the gauge fields production from the fermion backreaction, a phenomenon called Schwinger effect, thus jeopardizing their original capabilities. Using numerical methods, we study the backreaction on the generated gauge fields and revisit the processes of gauge preheating and baryogenesis in the presence of the Schwinger effect. We have found that gauge preheating is very unlikely, while still having a sizable window in the parameter space to achieve the baryon asymmetry of the Universe at the electroweak phase transition.

Impact of hypermagnetic fields on relic gravitational waves, neutrino oscillations and baryon asymmetry

In this paper, we study the evolution of random hypermagnetic fields (HMFs) in the symmetric phase of the early universe before the electroweak phase transition. The behavior of HMFs is driven by the analog of the chiral magnetic effect accounting for the asymmetries of leptons and Higgs bosons. These asymmetries are also dynamical variables of the model and evolve together with HMFs. Moreover, we account for the contribution of the hyper-MHD turbulence in the effective diffusion coefficient and the [Formula: see text]-dynamo parameter. The realistic spectrum of seed HMFs consists of two branches: Batchelor and Kolmogorov ones. The impact of HMFs on the production of relic gravitational waves (GWs) and the baryon asymmetry of the universe (BAU), as well as flavor oscillations of supernova neutrinos in the stochastic GWs generated is considered. We establish the constraint on the strength of the seed HMF comparing the spectral density of produced GWs with the observations of the LIGO-Virgo-KAGRA collaborations. The stronger upper bound on the seed HMF is obtained from the condition of not exceeding the observed value of BAU.

Electroweak phase transition in the presence of hypermagnetic field and the generation of gravitational waves

We investigate the effects of a large-scale background hypermagnetic field on the electroweak phase transition (EWPT). We propose a model in which an effective weak angle varies during the EWPT and upon its use we show that, although for the majority of the parameter space the phase transition is a crossover, there are tiny regions in which the phase transition occurs in two steps and can be first-order. We obtain all of the important quantities characterizing the details of the first-order phase transition, including the latent heat, transition temperature and duration. We then calculate the gravitational wave energy spectrum generated during the first-order part of the EWPT and find that, for strong enough background hypermagnetic fields, these signals can be detected by the Ultimate-DECIGO interferometer.

Hypermagnetogenesis from axion inflation: Model-independent estimates

Axion inflation coupled to the Standard Model (SM) hypercharge gauge sector represents an attractive scenario for the generation of primordial hypermagnetic fields. The description of this scenario is, however, complicated by the Schwinger effect, which gives rise to highly nonlinear dynamics. Hypermagnetogenesis during axion inflation in the absence of nonlinear effects is well studied and known to result in a hypermagnetic energy density that scales like $H^4\,e^{2\pi\xi}/\xi^5$, where $\xi$ is proportional to the time derivative of the axion-vector coupling in units of the Hubble rate $H$. In this paper, we generalize this result to the full SM case by consistently taking into account the Schwinger pair production of all SM fermions. To this end, we employ the novel gradient-expansion formalism that we recently developed in [2109.01651], and which is based on a set of vacuum expectation values for bilinear hyperelectromagnetic functions in position space. We parametrize the numerical output of our formalism in terms of three parameters ($\xi$, $H$, and $\Delta$, where the latter accounts for the damping of subhorizon gauge-field modes because of the finite conductivity of the medium) and work out semianalytical fit functions that describe our numerical results with high accuracy. Finally, we validate our results by comparing them to existing estimates in the literature as well as to the explicit numerical results in a specific inflationary model, which leads to good overall agreement. We conclude that the systematic uncertainties in the description of hypermagnetogenesis during axion inflation, which previously spanned up to several orders of magnitude, are now reduced to typically less than 1 order of magnitude, which paves the way for further phenomenological studies.

Gravitational waves generation in turbulent hypermagnetic fields before the electroweak phase transition

We study the production of relic gravitational waves (GWs) in turbulent hypermagnetic fields (HMFs) in the symmetric phase of the early universe before the electroweak phase transition (EWPT). The noise of HMFs is modeled by the analog of the magnetic hydrodynamics turbulence. The evolution of HMFs is driven by the analogs of the chiral magnetic effect and the Adler anomalies in the presence of the nonzero asymmetries of leptons and Higgs bosons. We track the evolution of the energy density of GWs from 10 TeV down to EWPT and analyze its dependence on the parameters of the system. We also discuss the possibility to observe the predicted GW background by the current GW detectors.

Magnetogenesis from baryon asymmetry during an early matter dominated era

In this paper, we study the simultaneous evolution of baryon asymmetry and hypermagnetic field amplitude assuming an early matter domination. We contrast our results to the conventional case where radiation domination during early universe is assumed. We show that the baryon asymmetry and the hypermagntic field amplitude can change by orders of magnitude if we assume a non-standard history of cosmology. That is because the Hubble rate determines which processes are efficient. We find that a change in Hubble rate can have a significant impact on when the weak sphalerons become active. As a result of a change in the evolution of baryonic asymmetry, alters the evolution of hypermagnetic field amplitude. It is known that if the hypermagnetic field amplitude is large enough, it can save the baryon asymmetry from diminishing. We show that whether a small seed of hypermagnetic field amplitude can be amplified to a large enough value will strongly depend on the history of cosmology.

Influence of non-ionizing radiation on protein metabolism in chickens

In practical terms, the idea of using an artificial magnetic field is of particular interest, which corresponds in its physical characteristics to the geomagnetic field of the Earth to combat the negative effects of hypogeomagnetic field. Further development of this idea is associated with the use and selection of hypo-, hypermagnetic fields acting on the body with experimental pathology. In this regard, the issue of influence of different duration of irradiation with an alternating pulsed electromagnetic field of ultra-low frequency (APEMF ULF) on the indicators that characterize metabolic processes in the body is insufficiently clarified. Therefore, the aim of research has been to study the effect of alternating pulsed electromagnetic field of ultra-low frequency on protein content and protein metabolism in the body of experimental chickens of the Dominant D959 cross. For this purpose, four experimental and control groups of 120-day-old chickens have been formed – 20 heads in each. The poultry has been kept in a specially equipped room with an alternating pulsed electromagnetic field of ultra-low frequency. The total protein content has been determined by the biuret method; protein fractions (albumins, globulins: alpha-1, alpha-2, beta, gamma) – by diffuse polyacrylamide gel (PAAG) electrophoresis; the content of creatinine, urea and uric acid has been performed by spectrophotometry using standard techniques. According to the results of research, it has been established that by selecting different regimens and duration of action of APEMF ULF, it is possible to influence protein metabolism in the body of chickens. Thus, on the 80th day of continuous irradiation of experimental chickens with APEMF ULF, regardless of the level of protein in the diet, in their blood revealed an increase in total protein, the relative content of globulin fraction mainly due to γ-globulins, and an increase in creatinine, urea and uric acids. When the period of continuous irradiation has been increased to 5 months, a negative effect on protein metabolism has been revealed, which has been manifested by a decrease in total protein content, relative albumin content, decrease in creatinine, urea and uric acid in the serum of experimental chickens. The combination of long-term (for 150 days) daily 60 minutes with weekly intervals of irradiation of chickens with APEMF ULF and their feeding with a 15% increase in protein levels in the diet caused a stimulating effect on protein metabolism and resistance of experimental chickens, with increasing, the relative content of globulins due to the γ-globulin fraction, as well as the main indicators of protein metabolism – creatinine, urea, uric acid. Key words: electromagnetic influence, chicken of Dominant D959 cross, total protein, protein fractions, creatinine, urea, uric acid.

Influence of the hypermagnetic field noise on the baryon asymmetry generation in the symmetric phase of the early universe

We study a matter turbulence caused by strong random hypermagnetic fields (HMFs) that influence the baryon asymmetry evolution due to the Abelian anomalies in the symmetric phase in the early Universe. Such a matter turbulence is stipulated by the presence of the advection term in the induction equation for which a fluid velocity is dominated by the Lorentz force in the Navier–Stokes equation. For random HMFs, having nonzero mean squared strengths, we calculate the spectra for the HMF energy and the HMF helicity densities. The latter function governs the evolution of the fermion asymmetries in the symmetric phase before the electroweak phase transition (EWPT). In the simplest model based on the first SM generation for the lepton asymmetries of e_mathrm {R,L} and nu _{e_mathrm {L}}, we calculate a decline of all fermion asymmetries including the baryon asymmetry, given by the ‘t Hooft conservation law, when one accounts for a turbulence of HMFs during the universe cooling down to EWPT. We obtain that the stronger the mean squared strength of random initial HMFs is, the deeper the fermion asymmetries decrease, compared to the case in the absence of any turbulence.

Geometrical aspects of hypermagnetic field interactions

We investigate the role of a dynamical torsion field coming from a geometrical non-Riemannian model. This model is reminiscent of a generalized Born-Infeld theory and the torsion plays a fundamental role trough its Hodge dual: the pseudovector This contains axion, Kalb-Ramond 2-form and physical observables of macroscopic character. An emergent interaction Lagrangian arises from the model and it is compared with a superstring inspired one taken from Bamba Kazuharu et al., Phys. Lett. B, 664 (2008) 154 pulling out several important consequences in favor of our proposal, as the possibility of establishing a clear connection between the change of the CMB polarization plane and the anomalous current .

Effects of nonhelical component of hypermagnetic field on the evolution of the matter-antimatter asymmetry, vorticity, and hypermagnetic field

We study the evolution of the matter-antimatter asymmetry ({\eta}), the vorticity, and the hypermagnetic field in the symmetric phase of the early Universe, and in the temperature range 100 GeV < T < 10 TeV. We assume a configuration for the hypermagnetic field which includes both helical and non-helical (Bz) components. Consequently, the hypermagnetic field and the fluid vorticity can directly affect each other, the manifestations of which we explore in three scenarios. In the first scenario, we show that in the presence of a small vorticity and a large {\eta}eR, helicity can be generated and amplified for an initially strong Bz. The generation of the helical seed is due to the chiral vortical effect (CVE) and/or the advection term, while its growth is mainly due to the chiral magnetic effect (CME) which leads to the production of the baryon asymmetry, as well. The vorticity saturates to a nonzero value which depends on Bz, even in the presence of the viscosity, due to the back-reaction of Bz on the plasma. Increasing the initial vorticity, makes the values of the helicity, {\eta}s, and vorticity reach their saturation curves sooner, but does not change their final values at the onset of the electroweak phase transition. The second scenario is similar to the first except we assume that all initial {\eta}s are zero. We find that much higher initial vorticity is required for the generation process. In the third scenario, we show that in the presence of only a strong hypermagnetic field, {\eta}s and vorticity can be generated and amplified. Increasing the initial helicity, increases the final {\eta}s and vorticity. We find that although the presence of a nonzero initial Bz is necessary in all three scenarios, its increase only increases the final values of vorticity.

Born-Infeld generalization: Axion and Kalb-Ramond from dynamical torsion fields

We show that in theories of gravitation based on affine geometries the torsion field, that takes a dynamical character, not only the chiral magnetic effect (CME) intervenes in the wash up of the chiral anomaly but also the chiral vortical effect (CVE) and the coupled chiral effect (CCE) coming from the hypermagnetic field interaction with the primordial plasma are crucial in a realistic physical scenario, as in the case of the early universe. We also show that the equation governing the wash up takes the form given in this paper, supplemented with the dynamical equation for the torsion vector containing the helicities and other axial couplings. The role played by the neutrinos in the interaction with the axion field in this theoretical framework is briefly discussed.

The generation of matter\u2013antimatter asymmetries and hypermagnetic fields by the chiral vortical effect of transient fluctuations

We study the contribution of the temperature-dependent chiral vortical effect to the generation and evolution of hypermagnetic fields and matter-antimatter asymmetries, in the symmetric phase of the early Universe, in the temperature range 100 GeV le T le 10 TeV. Our most important result is that, due to the chiral vortical effect, small overlapping transient fluctuations in the vorticity field in the plasma and temperature of matter degrees of freedom can lead to the generation of strong hypermagnetic fields and matter-antimatter asymmetries, all starting from zero initial values. We show that, either an increase in the amplitudes of the fluctuations of vorticity or temperature, or a decrease in their widths, leads to the production of stronger hypermagnetic fields, and therefore, larger matter-antimatter asymmetries. We have the interesting result that fluctuating vorticity fields are more productive, by many orders of magnitude, as compared to vorticities that are constant in time.

Flavon magnetobaryogenesis

In this paper, we explore the evolution of baryon asymmetry as well as the hypermagnetic field in the early universe with an assumption that the flavon of the Froggatt-Nielsen carries an asymmetry. Through the decay of the flavon to Standard Model fermions, this asymmetry is transferred to fermions, where the right-handed electron keeps its asymmetry while its Yukawa interaction is out of thermal equilibrium. Through the existence of the flavon, we can ensure that the freezing-in temperature of the right-handed electron is closer to the electroweak phase transition than the Standard cosmology scenario. With this trick, the asymmetry in the right-handed electron is saved for a longer time. Moreover, the injection of the asymmetry to the right-handed electron is gradual, which helps the preservation of the asymmetry in the right-handed sector significantly. Due to the intimate relationship between fermion number violation and the helicity of the hypermagnetic field, some of the asymmetry is used to amplify the hypermagnetic field which itself helps to preserve the remnant asymmetry through keeping the Yukawa processes out of thermal equilibrium. We find the sweet region of the parameter space that can produce the right asymmetry in the baryons while generating a large hypermagnetic field by the time of the electroweak phase transition.

Contribution of the chiral vortical effect to the evolution of the hypermagnetic field and the matter-antimatter asymmetry in the early Universe

In this paper, we study the contribution of the chiral vortical effect, in addition to that of the chiral magnetic effect, to the evolution of the hypermagnetic field and the matter-antimatter asymmetry in the symmetric phase of the early Universe in the temperature range 100GeV < T < 10TeV. We choose a fully helical Chern-Simons wave configuration for the velocity and the hypermagnetic vector potential fields. The latter makes the plasma force-free in the absence of viscosity. We show that the most pronounced effect of the chiral vorticity is the production and initial growth of the hypermagnetic field. In particular, we show that in the presence of a non-zero matter asymmetry, the hypermagnetic field can grow from zero initial value only in the presence of a non-zero vorticity field. Moreover, we show that larger initial growths not only result in larger maximum values of the hypermagnetic field, but also cause the saturation of the hypermagnetic field and the conversion of the lepton-baryon asymmetry to occur more quickly, i.e., at a higher temperature. We show that the damping of the vorticity due to the presence of viscosity, which typically occurs extremely rapidly, does not significantly affect the evolution.

Baryogenesis from axion inflation

The coupling of an axion-like particle driving inflation to the Standard Model particle content through a Chern-Simons term generically sources a dual production of massless helical gauge fields and chiral fermions. We demonstrate that the interplay of these two components results in a highly predictive baryogenesis model, which requires no further ingredients beyond the Standard Model. If the helicity stored in the hyper magnetic field and the effective chemical potential induced by the chiral fermion production are large enough to avoid magnetic diffusion from the thermal plasma but small enough to sufficiently delay the chiral plasma instability, then the non-vanishing helicity survives until the electroweak phase transition and sources a net baryon asymmetry which is in excellent agreement with the observed value. If any of these two conditions is violated, the final baryon asymmetry vanishes. The observed baryon asymmetry can be reproduced if the energy scale of inflation is around Hinf ∼ 1010–1012 GeV with a moderate dependence on inflation model parameters.

Minimal system including weak sphalerons for investigating the evolution of matter asymmetries and hypermagnetic fields

We study simultaneous evolution of large scale hypermagnetic fields and the asymmetries of quarks, leptons and Higgs boson in the temperature range from 10TeV to 100GeV. Above 10TeV, we identify all of the major fast interactions and use the associated conservation laws as constraints on the initial conditions at 10TeV. Below 10TeV, we identify the major processes which fall out of equilibrium or emerge as non-negligible processes and derive the relevant evolution equations. These include the Abelian anomalies which violate fermion numbers, direct and inverse Higgs decays that change the chiralities of fermions, and weak sphalerons which violate the left-handed fermion numbers. We also consider the contributions of all fermionic chemical potentials to the UY(1) Chern-Simons term which affects the evolution through the AMHD equations. Thus, we present a minimal set of self-consistent initial conditions and evolution equations which respect all constraints coming from conservation laws, fast processes and charge neutrality of the plasma. We solve the coupled evolution equations and find that initial large hypermagnetic field can produce matter asymmetries starting from zero initial value, and vice versa provided an initial seed of hypermagnetic field is present and the rate of the electron Yukawa processes is lower. We find that our model yields acceptable values for baryon asymmetry and magnetic field. However, the scale of the magnetic field obtained is much smaller than the observational data, even when the turbulence driven inverse cascade mechanism in the broken phase is taken into account.