Large-scale magnetic fields from inflation in dilaton electromagnetism

TL;DR

The paper addresses the origin of large-scale cosmological magnetic fields by breaking Maxwell conformal invariance through a dilaton–photon coupling during inflation. It develops a two-field inflationary framework where the dilaton field modulates the electromagnetic sector via f(Φ) = exp(λ κ Φ), deriving the mode evolution of the vector potential and identifying a key parameter β that controls the spectrum. The authors show that a nearly scale-invariant spectrum (|β| ≈ 5) can yield present-day magnetic fields in the range 10^{-10}–10^{-9} G on Mpc scales, even when substantial entropy production occurs from dilaton decay, provided the ratio X = λ/tilde{λ} is large. They analyze both slow-roll exponential and power-law inflation, and find that achieving the required spectrum generally demands a strong hierarchy in the couplings, which poses model-building challenges. Overall, their results suggest a viable, though parameter-sensitive, inflationary magnetogenesis mechanism with implications for the origin of galactic and cluster magnetic fields.

Abstract

The generation of large-scale magnetic fields is studied in dilaton electromagnetism in inflationary cosmology, taking into account the dilaton's evolution throughout inflation and reheating until it is stabilized with possible entropy production. It is shown that large-scale magnetic fields with observationally interesting strength at the present time could be generated if the conformal invariance of the Maxwell theory is broken through the coupling between the dilaton and electromagnetic fields in such a way that the resultant quantum fluctuations in the magnetic field has a nearly scale-invariant spectrum. If this condition is met, the amplitude of the generated magnetic field could be sufficiently large even in the case huge amount of entropy is produced with the dilution factor $\sim 10^{24}$ as the dilaton decays.

Figures (5)

• Figure 1: The curves (dotted lines and a solid line) in the $H_\mathrm{inf}-\beta$ parameter space on which the present magnetic fields on 1Mpc scale with each strength could be generated ( $\beta>0$ ). $B(t_0)=10^{-9} \mathrm{G}$, $10^{-10} \mathrm{G}$, $10^{-16} \mathrm{G}$, $10^{-22} \mathrm{G}$ (solid line), $10^{-30} \mathrm{G}$, $10^{-40} \mathrm{G}$, and $10^{-50} \mathrm{G}$ are shown (top down). The shaded area illustrates the excluded region from the observation of the anisotropy of CMB, Eq. (\ref{['eq:71']}).
• Figure 2: The curves (dotted lines and a solid line) in the $H_\mathrm{inf}-\beta$ parameter space on which the present magnetic fields on 1Mpc scale with each strength could be generated ( $\beta<0$ ). $B(t_0)=10^{-9} \mathrm{G}$, $10^{-10} \mathrm{G}$, $10^{-16} \mathrm{G}$, $10^{-22} \mathrm{G}$ (solid line), $10^{-30} \mathrm{G}$, $10^{-40} \mathrm{G}$, and $10^{-50} \mathrm{G}$ are shown (top down). The shaded area corresponds to $\Upsilon \geq 1$ and illustrates the excluded region from the consistency condition decided by Eq. (\ref{['eq:65']}). This area includes the excluded region from the observation of the anisotropy of CMB.
• Figure 3: The magnetic field strength on 1Mpc scale at the present time $\tilde{B}(t_0)$ in the case with entropy production. The lines are for the case $H_\mathrm{inf} = 10^{14} \mathrm{GeV}$ and $m=10^{13} \mathrm{GeV}$. $\beta \approx 1 + \lambda \tilde{\lambda} w \approx 5.0$, $\beta \approx 4.5$, $\beta \approx 4.0$, and $\beta \approx 3.5$ are shown (top down). Here we have taken $w =0.01$ and ${\tilde{\lambda}} \sim \mathcal{O}(1)$.
• Figure 4: The magnetic field strength on 1Mpc scale at the present time $\tilde{B}(t_0)$ in the case with entropy production. The lines are for the case $H_\mathrm{inf} = 10^{10} \mathrm{GeV}$ and $m=10^{9} \mathrm{GeV}$. $\beta \approx 1 + \lambda \tilde{\lambda} w \approx 5.0$, $\beta \approx 4.5$, $\beta \approx 4.0$, and $\beta \approx 3.5$ are shown (top down). Here we have taken $w =0.01$ and ${\tilde{\lambda}} \sim \mathcal{O}(1)$.
• Figure 5: The curves (dotted lines and a solid line) in the $H_\mathrm{inf}-m$ parameter space on which the present magnetic fields on 1Mpc scale with each strength could be generated for the case $\beta \approx 5.0$. $\tilde{B}(t_0)=10^{-9} \mathrm{G}$, $10^{-10} \mathrm{G}$, $10^{-16} \mathrm{G}$, $10^{-22} \mathrm{G}$ (solid line), and $10^{-30} \mathrm{G}$ are shown (top down). The shaded area illustrates the region with $m > 2H_\mathrm{inf}$, where $t_\mathrm{R} > t_\mathrm{osc}$ and our analysis does not apply. Here we have taken the maximum of $\tilde{\lambda} \kappa |{\Phi}_\mathrm{R}|$ for each case, and $w =0.01$ and ${\tilde{\lambda}} \sim \mathcal{O}(1)$.