Provided the quantum fluctuations are amplified in the presence of a classical gauge field configuration the resulting curvature perturbations exhibit a mild statistical anisotropy which should be sufficiently weak not to conflict with current observational data. The curvature power spectra induced by weakly anisotropic initial states are computed here for the first time when the electric and the magnetic gauge couplings evolve at different rates as it happens, for instance, in the relativistic theory of van der Waals interactions. After recovering the results valid for coincident gauge couplings, the constraints imposed by the isotropy and the homogeneity of the initial states are discussed. The obtained bounds turn out to be more stringent than naively expected and cannot be ignored when discussing the underlying magnetogenesis scenarios.
The $R^2$ term in the Starobinsky inflationary model can be regarded as a leading quantum correction to the gravitational effective action. We assume that parity-preserving and parity-violating (axial) non-minimal couplings between curvature and electromagnetic field are also present in the effective action. In the Einstein frame, they turn into non-trivial couplings of the scalaron and curvature to the electromagnetic field. We make an assessment of inflationary magnetogenesis in this model. In the case of parity-preserving couplings, amplification of magnetic field is negligibly small. In th…
The effective approach is applied to the analysis of inflationary magnetogenesis. Rather than assuming a particular underlying description, all the generally covariant terms potentially appearing with four space-time derivatives in the effective action have been included and weighted by inflaton-dependent couplings. The higher derivatives are suppressed by the negative powers of a typical mass scale whose specific values ultimately depend on the tensor to scalar ratio. During a quasi-de Sitter stage the corresponding corrections always lead to an asymmetry between the hypermagnetic and the hyp…
We derive a simple model-independent upper bound on the strength of magnetic fields obtained in inflationary and post-inflationary magnetogenesis taking into account the constraints imposed by the condition of weak coupling, back-reaction and Schwinger effect. This bound turns out to be rather low for cosmologically interesting spatial scales. Somewhat higher upper bound is obtained if one assumes that some unknown mechanism suppresses the Schwinger effect in the early universe. Incidentally, we correct our previous estimates for this case.
We consider helical coupling to electromagnetism and present a simple scenario of evolution of the coupling function leading to a viable inflationary magnetogenesis without the problem of back-reaction. In this scenario, helical magnetic fields of strength of order up to $10^{- 7}\,\text{G}$, when extrapolated to the current epoch, can be generated in a narrow spectral band centered at any reasonable wavenumber by adjusting the model parameters. We discuss implications of this model for baryogenesis, which impose additional constraints on the strength and correlation length of magnetic field.
We describe a simple scenario of inflationary magnetogenesis based on a helical coupling to electromagnetism. It allows to generate helical magnetic fields of strength of order up to $10^{- 7}\,\text{G}$, when extrapolated to the current epoch, in a narrow spectral band centered at any physical wavenumber by adjusting the model parameters. Additional constraints on magnetic fields arise from the considerations of baryogenesis and, possibly, from the Schwinger effect of creation of charged particle-antiparticle pairs.
Large-scale magnetogenesis is analyzed within the Palatini approach when the gravitational action is supplemented by a contribution that is nonlinear in the Einstein-Hilbert term. While the addition of the nonlinear terms does not affect the scalar modes of the geometry during the inflationary phase, the tensor-to-scalar ratio is nonetheless suppressed. In this context it is plausible to have a stiff phase following the standard inflationary stage provided the potential has a quintessential form. The large-scale magnetic fields can even be a fraction of the nG over typical length scales of the…
Inflationary magnetogenesis from non-minimal coupling in large- and small-field potentials
Università di Camerino（卡梅里诺大学）；University at Albany-SUNY（奥尔巴尼州立大学（纽约州立大学））；INAF - Osservatorio Astronomico di Brera（意大利国家天体物理研究所布雷拉天文台）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Perugia（意大利国家核物理学院佩鲁吉亚分部）
We show that breaking of the conformal invariance of electromagnetic Lagrangian which is required for inflationary magnetogenesis arises naturally in the Poincar{é} Gauge Theory. We use the minimal coupling prescription to introduce the electromagnetic gauge fields as well as non-abelian gauge fields in this theory. Due to the addition of non-abelian gauge fields, we show that the solar constraints on this model can be naturally evaded. We find that in the minimal version of this model the generated magnetic field is too small to explain the observations. We discuss some generalizations of the…
While during inflation a phase of increasing gauge coupling allows for a scale-invariant hyperelectric spectrum, when the coupling decreases a flat hypermagnetic spectrum can be generated for typical wavelengths larger than the effective horizon. After the gauge coupling flattens out the late-time hypermagnetic power spectra outside the horizon in the radiation epoch are determined by the hyperelectric fields at the end of inflation whereas the opposite is true in the case of decreasing coupling. Instead of imposing an abrupt freeze after inflation, we consider a smooth evolution of the mode f…
In previous work, two of us have proposed a model of inflationary magnetogenesis based on a rolling auxiliary field able both to account for the magnetic fields inferred by the (non) observation of gamma-rays from blazars, and to start the galactic dynamo, without incurring in any strong coupling or strong backreaction regime. Here we evaluate the correction to the scalar spectrum and bispectrum with respect to single-field slow-roll inflation generated in that scenario. The strongest constraints on the model originate from the non-observation of a scalar bispectrum. Nevertheless, even when th…
Cosmological inflation provides the initial conditions for the structure formation. However, the origin of large-scale magnetic fields cannot 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 act…
The simplest model of primordial magnetogenesis can provide scale-invariant magnetic fields that can explain the present abundances of it in the cosmic scales. Two kinds of solutions of the coupling function can lead to such phenomena and both of them suffer from the problems of either strong-coupling or large backreaction. In this work, we consider the coupling function as a linear combination of both kinds with a model parameter. We find that the parameter needs to be as small as $\sim 10^{-20}$ in order to evade the backreaction problem. On the other hand, requiring that the modes above Mpc…
Using numerical simulations of helical inflationary magnetogenesis in a low reheating temperature scenario, we show that the magnetic energy spectrum is strongly peaked at a particular wavenumber that depends on the reheating temperature. Gravitational waves (GWs) are produced at frequencies between 3 nHz and 50 mHz for reheating temperatures between 150 MeV and 3x10^5 GeV, respectively. At and below the peak frequency, the stress spectrum is always found to be that of white noise. This implies a linear increase of GW energy per logarithmic wavenumber interval, instead of a cubic one, as previ…
We present three-dimensional direct numerical simulations of the production of magnetic fields and gravitational waves (GWs) in the early Universe during a low energy scale matter-dominated post-inflationary reheating era, and during the early subsequent radiative era, which is strongly turbulent. The parameters of the model are determined such that it avoids a number of known physical problems and produces magnetic energy densities between 0.2% and 2% of the critical energy density at the end of reheating. During the subsequent development of a turbulent magnetohydrodynamic cascade, magnetic …
Effective theory framework based on symmetry has recently gained widespread interest in the field of cosmology. In this paper, we apply the same idea on the genesis of the primordial magnetic field and its evolution throughout the cosmological universe. Given the broken time-diffeomorphism symmetry by the cosmological background, we considered the most general Lagrangian of electromagnetic and metric fluctuation up to second order, which naturally breaks conformal symmetry in the electromagnetic (EM) sector. We also include parity violation in the electromagnetic sector with the motivation tha…
We study the generation of magnetic fields during inflation making use of a coupling of the inflaton and moduli fields to electromagnetism via the photon kinetic term, and assuming that the coupling is an increasing function of time. We demonstrate that the strong coupling problem of inflationary magnetogenesis can be avoided by incorporating the destabilization of moduli fields after inflation. The magnetic field always dominates over the electric one, and thus the severe constraints on the latter from backreaction, which are the demanding obstacles in the case of a decreasing coupling functi…
We study the generation of helical magnetic fields in a model of inflationary magnetogenesis which is free from the strong coupling and back-reaction problems. To generate helical magnetic fields, we add an $f^2 \tilde{F}^{μν} F_{μν}$ term to the lagrangian of Ratra model. The strong coupling and back-reaction problems are avoided if we take a particular behaviour of coupling function $f$, in which $f$ increases during inflation and decreases post inflation to reheating. The generated magnetic field is fully helical and has a blue spectrum, $dρ_B/d\ln k \propto k^4$. This spectrum is obtained …
Generation of magnetic field during inflation can explain its presence over a wide range of scales in the Universe. In Ref.\cite{sharma2017}, we proposed a model to generate these fields during inflation. These fields have nonzero anisotropic stress which lead to the generation of a stochastic background of gravitational waves (GW) in the early universe. Here we show that for a scenario of magnetogenesis where reheating takes place around QCD epoch, this stochastic GW background lies in the $95\%$ confidence region of the GW signal probed by NANOGrav collaboration. This is the case when the ge…
Primordial magnetic fields are generated during inflation by considering actions that break the conformal invariance of the electromagnetic field. To break the conformal invariance, the electromagnetic fields are coupled either to the inflaton or to the scalar curvature. Also, a parity violating term is often added to the action in order to enhance the amplitudes of the primordial electromagnetic fields. In this work, we examine the effects of deviations from slow roll inflation on the spectra of non-helical as well as helical electromagnetic fields. We find that, in the case of the coupling t…
Generation of magnetic fields during inflation is a promising mechanism for the origin of the observed large scale magnetic fields in the universe. Among several attempts, a popular model is one where the inflaton and the electromagnetic field are coupled through a coupling function $f$ leading to a term in the Lagrangian density of the form, $f^2 F^{μν} F_{μν}$. A number of potential difficulties with such models have been raised in the literature. In our earlier work, we have suggested viable models of inflationary magnetogenesis which avoid these problems and at the same time can lead to ei…
[Abridged] As is well known, in order to generate magnetic fields of observed amplitudes during inflation, the conformal invariance of the electromagnetic field has to be broken by coupling it either to the inflaton or to the scalar curvature. Couplings to scalar curvature pose certain challenges even in slow roll inflation and it seems desirable to consider couplings to the inflaton. It can be shown that, in slow roll inflation, to generate nearly scale invariant magnetic fields of adequate strengths, the non-conformal coupling to the inflaton has to be chosen specifically depending on the in…
We study the generation of electromagnetic fields during inflation when the conformal invariance of Maxwell's action is broken by the kinetic coupling $f^{2}(ϕ)F_{μν}F^{μν}$ of the electromagnetic field to the inflaton field $ϕ$. We consider the case where the coupling function $f(ϕ)$ decreases in time during inflation and, as a result, the electric component of the energy density dominates over the magnetic one. The system of equations which governs the joint evolution of the scale factor, inflaton field, and electric energy density is derived. The backreaction occurs when the electric energy…
