[Paper Review] Thermal enhancement of inflationary magnetic fields

Arjun Berera, Suddhasattwa Brahma+2 more|arXiv (Cornell University)|Mar 10, 2026

Cosmology and Gravitation Theories0 citations

TL;DR

The paper shows that a thermal initial state for the gauge field during inflation can significantly boost primordial magnetic fields by changing their redshift from a^{-4} to a^{-3}, motivating embedding in a warm inflation framework, though not enough alone to meet all observational bounds.

ABSTRACT

We investigate primordial magnetogenesis by assuming the gauge field is prepared in a thermal state during inflation rather than the standard Bunch-Davies vacuum. The temperature $\mathcal{T}$ introduces a physical scale that breaks conformal invariance at the level of the state while preserving the standard Maxwell action. This modification results in a {\it dissipative boost} that alters the magnetic energy density scaling from $a^{-4}$ to $a^{-3}$, resulting in a present-day magnetic field $B_0$ enhancement that can potentially range from about $10^{8}$ to $10^{16}$ on galactic scales. While this toy model alone does not satisfy observational lower bounds, it demonstrates that thermal initial conditions can significantly mitigate the conformal obstruction. Our results suggest that embedding this mechanism within a fully dynamical warm inflation framework, where dissipation continuously maintains the thermal bath, provides a highly promising path towards successfully realizing a minimal model of inflationary magnetogenesis without the need to invoke non-minimal couplings, anomalous background dynamics or nonlinear extensions of electrodynamics.

Motivation & Objective

• Motivate and quantify magnetogenesis with the gauge field in a thermal state during inflation.
• Explain how a constant physical temperature during inflation breaks conformal invariance at the state level and alters spectra.
• Compute the thermally corrected magnetic spectrum and its evolution to present-day fields.
• Assess whether this mechanism can evade standard no-go bounds and its implications for warm inflation.

Proposed method

• Assume the gauge field is in a thermal state with comoving temperature T and Bose-Einstein occupation numbers.
• Derive the thermally corrected magnetic energy spectrum: dρ_B/dln k = (k^4/4π^2 a^4) coth(k/(2aT)).
• Show that in the super-horizon (IR) limit the spectrum yields ρ_B ∝ k^3 T/(a^3), implying a decay ∝ a^{-3} rather than a^{-4}.
• Define B_λ = sqrt(2 dρ_B/dln k) and relate end-of-inflation scales to present-day fields, including the dissipative boost r_therm/r_vac.
• Discuss embedding this toy model into a full warm-inflation framework where dissipation maintains the thermal bath, rather than instantaneous reheating.

Figure 1 : Thermal correction factor $\coth(\frac{k}{2a\mathcal{T}})$ compared with the Rayleigh-Jeans approximation of the full curve is plotted as a function of the dimensionless ratio $\log_{10}\frac{k_{c}^{*}}{k_{c}}$ . $\lambda^{*}_{c}=\frac{2\pi a}{k_{c}^{*}}$ is the pivot scale introduced sat

Experimental results

Research questions

• RQ1 Can a thermal initial state of the gauge field enhance inflationary magnetic fields without modifying the Maxwell action?
• RQ2 How does a constant physical temperature during inflation modify the magnetic spectrum and its later redshift compared to the vacuum case?
• RQ3 To what extent can thermal initial conditions help circumvent Green-Kobayashi-type no-go bounds for inflationary magnetogenesis?
• RQ4 What are the observational implications and required conditions for embedding this mechanism in a full warm inflation setup?

Key findings

• Thermal occupation introduces a coth(k/(2aT)) factor, enhancing the magnetic spectrum relative to the vacuum state.
• The magnetic energy density decays as a^{-3} during inflation, rather than a^{-4}, due to the sustained thermal bath.
• On 10 kpc scales with T ≈ 10^10 GeV, the present-day field strength is predicted around 10^{-41} G, a huge enhancement over the vacuum expectation (~10^{-53} G).
• On 1 Mpc scales, the thermally enhanced field is ~10^{-44} G, still below the astrophysical lower bounds but markedly boosted (r_therm/r_vac up to ~10^{24}–10^{32} depending on parameters).
• In a fully dynamical warm inflation setting with T ≈ T_reh, the enhancement becomes largely independent of M_inf and T_reh, and the dissipative boost scales roughly as (T/H_inf) e^N.