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Adding helicity to inflationary magnetogenesis

Chiara Caprini, Lorenzo Sorbo

TL;DR

The paper addresses the challenge of generating cosmological magnetic fields during inflation without backreaction or strong coupling by introducing a time-dependent coefficient $I( au)$ that multiplies both the Maxwell term $F_{\mu\nu}F^{\mu\nu}$ and a parity-violating term $F_{\mu\nu}\tilde{F}^{\mu\nu}$. This hybrid Ratra-axion approach yields a maximally helical field whose amplitude is exponentially sensitive to the coupling parameter $\\xi$, and an inverse cascade transfers power to large scales, making it feasible to satisfy IGM lower bounds and seed galactic dynamos for inflation scales in the range $10^5$–$10^{10}$ GeV. A crucial result is that gauge-field–sourced tensors can produce a sizable tensor-to-scalar ratio $r$ even at low $H$, thereby evading the Lyth bound; the model also predicts a chiral spectrum of primordial gravitational waves and parity-odd CMB correlations ($\\langle TB\\rangle$, $\\langle EB\\rangle$). The work discusses observational constraints, potential UV completions (supergravity and brane inflation), and distinctive signatures of fully helical magnetic fields and parity-violating gravitational waves that could be tested with future data.

Abstract

The most studied mechanism of inflationary magnetogenesis relies on the time-dependence of the coefficient of the gauge kinetic term $F_{μν}\,{F}^{μν}$. Unfortunately, only extremely finely tuned versions of the model can consistently generate the cosmological magnetic fields required by observations. We propose a generalization of this model, where also the pseudoscalar invariant $F_{μν}\,\tilde{F}^{μν}$ is multiplied by a time dependent function. The new parity violating term allows more freedom in tuning the amplitude of the field at the end of inflation. Moreover, it leads to a helical magnetic field that is amplified at large scales by magnetohydrodynamical processes during the radiation dominated epoch. As a consequence, our model can satisfy the observational lower bounds on fields in the intergalactic medium, while providing a seed for the galactic dynamo, if inflation occurs at an energy scale ranging from $10^5$ to $10^{10}$ GeV. Such energy scale is well below that suggested by the recent BICEP2 result, if the latter is due to primordial tensor modes. However, the gauge field is a source of tensors during inflation and generates a spectrum of gravitational waves that can give a sizable tensor to scalar ratio $r={\cal O}(0.2)$ even if inflation occurs at low energies. This system therefore evades the Lyth bound. For smaller values of $r$, lower values of the inflationary energy scale are required. The model predicts fully helical cosmological magnetic fields and a chiral spectrum of primordial gravitational waves.

Adding helicity to inflationary magnetogenesis

TL;DR

The paper addresses the challenge of generating cosmological magnetic fields during inflation without backreaction or strong coupling by introducing a time-dependent coefficient that multiplies both the Maxwell term and a parity-violating term . This hybrid Ratra-axion approach yields a maximally helical field whose amplitude is exponentially sensitive to the coupling parameter , and an inverse cascade transfers power to large scales, making it feasible to satisfy IGM lower bounds and seed galactic dynamos for inflation scales in the range – GeV. A crucial result is that gauge-field–sourced tensors can produce a sizable tensor-to-scalar ratio even at low , thereby evading the Lyth bound; the model also predicts a chiral spectrum of primordial gravitational waves and parity-odd CMB correlations (, ). The work discusses observational constraints, potential UV completions (supergravity and brane inflation), and distinctive signatures of fully helical magnetic fields and parity-violating gravitational waves that could be tested with future data.

Abstract

The most studied mechanism of inflationary magnetogenesis relies on the time-dependence of the coefficient of the gauge kinetic term . Unfortunately, only extremely finely tuned versions of the model can consistently generate the cosmological magnetic fields required by observations. We propose a generalization of this model, where also the pseudoscalar invariant is multiplied by a time dependent function. The new parity violating term allows more freedom in tuning the amplitude of the field at the end of inflation. Moreover, it leads to a helical magnetic field that is amplified at large scales by magnetohydrodynamical processes during the radiation dominated epoch. As a consequence, our model can satisfy the observational lower bounds on fields in the intergalactic medium, while providing a seed for the galactic dynamo, if inflation occurs at an energy scale ranging from to GeV. Such energy scale is well below that suggested by the recent BICEP2 result, if the latter is due to primordial tensor modes. However, the gauge field is a source of tensors during inflation and generates a spectrum of gravitational waves that can give a sizable tensor to scalar ratio even if inflation occurs at low energies. This system therefore evades the Lyth bound. For smaller values of , lower values of the inflationary energy scale are required. The model predicts fully helical cosmological magnetic fields and a chiral spectrum of primordial gravitational waves.

Paper Structure

This paper contains 7 sections, 27 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Production of electromagnetic fields during inflation
  3. Electromagnetic fields, low scale inflation and the Lyth bound
  4. Inverse cascade and the current intensity of the magnetic field
  5. Observational constraints
  6. Two simple models: supergravity and brane inflation
  7. Conclusions

Figures (4)

  • Figure 1: The function $p^t(n)$ appearing in equation (\ref{['ptem']}) that determines the amplitude of the tensor spectrum induced by the magnetic field.
  • Figure 2: The evolution of the comoving magnetic correlation scale as a function of temperature, for $n=-1.9$ and $\xi=13$, corresponding to an inflationary energy scale $\rho_{\rm {inf}}^{1/4}\simeq 3\times 10^9$ GeV. The red, dashed curve represents the comoving neutrino mean free path, and the green, dot-dashed curve the photon one. The jump in $L_c(T)$ at recombination is due to the sudden increase of the photon mean free path just before decoupling, caused by the drop in the ionization fraction. The alternating phases of turbulent, viscous, and free-streaming evolution are apparent. The evolution of $B$ is obtained straightforwardly from that of $L$ by imposing conservation of helicity.
  • Figure 3: Solid, top to bottom: inflationary energy scale, as a function of the parameter $n$, necessary for the generation of a magnetic field of $6\times 10^{-18}$ G (the lower bound quoted by Vovk:2011aa), $2.5\times 10^{-17}$ G and $10^{-16}$ G times $\sqrt{1\,{\mathrm {Mpc}}/L_0}$, assuming a tensor-to-scalar ratio $r=0.2$. Dashed line: inflationary energy scale, as a function of the parameter $n$, necessary for the generation of a magnetic field of $2.5\times 10^{-17}$ G at scales of $1$ Mpc, assuming a tensor-to-scalar ratio $r=10^{-4}.$
  • Figure 4: Solid lines: intensity of the magnetic field at $1$ Mpc scale, as a function of the parameter $n$, obtained by imposing that the magnetic field at the correlation scale $L_0$ satisfies the observational lower bound in the IGM: from top to bottom, $6\times 10^{-18}$ G (the lower bound quoted by Vovk:2011aa), $2.5\times 10^{-17}$ G and $10^{-16}$ G times $\sqrt{1\,{\mathrm {Mpc}}/L_0}$. As in figure \ref{['fig:hubnv']}, we assume a tensor-to-scalar ratio $r=0.2$. The kink at $n=-0.5$ originates from the absolute value in the spectral index, eq. (\ref{['nb']}). The two horizontal dashed lines correspond to the weaker ($10^{-23}$ G) and stronger ($10^{-21}$ G) requirements for the field intensities able to seed the galactic dynamo.