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Universal upper limit on inflation energy scale from cosmic magnetic field

Tomohiro Fujita, Shinji Mukohyama

TL;DR

The paper addresses whether inflation can generate the observed cosmic magnetic fields and derives a universal upper bound on the inflation energy scale under four plausible assumptions, linking magnetic-field observations to $\rho_{\rm inf}^{1/4}$ via $\rho_{\rm inf}^{1/4} < 2.5 \times 10^{-7} M_{\rm Pl} \left( \dfrac{B_{\rm obs}}{10^{-15}\ \,\text{G}} \right)^{-2}$.The authors present a model-independent derivation that does not rely on specific inflaton or photon-mode dynamics, but requires: (i) a photon kinetic term with a time-dependent factor, (ii) no strong coupling, (iii) small back reaction during inflation, and (iv) magnetogenesis occurring during inflation.A tensor-to-scalar ratio bound $r < 10^{-19} \left( \dfrac{B_{\rm obs}}{10^{-15}\ \text{G}} \right)^{-8}$ follows, implying that if $B_{\rm obs} \gtrsim 10^{-15}$ G and gravitational waves are detected soon, inflationary magnetogenesis would be in tension with observations.The paper also analyzes alternative interaction terms and argues that viable cancellations required to evade the bound are difficult to realize, making the result a strong guideline for constructing magnetogenesis models.

Abstract

Recently observational lower bounds on the strength of cosmic magnetic fields were reported, based on gamma-ray flux from distant blazars. If inflation is responsible for the generation of such magnetic fields then the inflation energy scale is bounded from above as rho_{inf}^{1/4} < 2.5 times 10^{-7}M_{Pl} times (B_{obs}/10^{-15}G)^{-2} in a wide class of inflationary magnetogenesis models, where B_{obs} is the observed strength of cosmic magnetic fields. The tensor-to-scalar ratio is correspondingly constrained as r< 10^{-19} times (B_{obs}/10^{-15}G)^{-8}. Therefore, if the reported strength B_{obs} \geq 10^{-15}G is confirmed and if any signatures of gravitational waves from inflation are detected in the near future, then our result indicates some tensions between inflationary magnetogenesis and observations.

Universal upper limit on inflation energy scale from cosmic magnetic field

TL;DR

The paper addresses whether inflation can generate the observed cosmic magnetic fields and derives a universal upper bound on the inflation energy scale under four plausible assumptions, linking magnetic-field observations to $\rho_{\rm inf}^{1/4}$ via $\rho_{\rm inf}^{1/4} < 2.5 \times 10^{-7} M_{\rm Pl} \left( \dfrac{B_{\rm obs}}{10^{-15}\ \,\text{G}} \right)^{-2}$.The authors present a model-independent derivation that does not rely on specific inflaton or photon-mode dynamics, but requires: (i) a photon kinetic term with a time-dependent factor, (ii) no strong coupling, (iii) small back reaction during inflation, and (iv) magnetogenesis occurring during inflation.A tensor-to-scalar ratio bound $r < 10^{-19} \left( \dfrac{B_{\rm obs}}{10^{-15}\ \text{G}} \right)^{-8}$ follows, implying that if $B_{\rm obs} \gtrsim 10^{-15}$ G and gravitational waves are detected soon, inflationary magnetogenesis would be in tension with observations.The paper also analyzes alternative interaction terms and argues that viable cancellations required to evade the bound are difficult to realize, making the result a strong guideline for constructing magnetogenesis models.

Abstract

Recently observational lower bounds on the strength of cosmic magnetic fields were reported, based on gamma-ray flux from distant blazars. If inflation is responsible for the generation of such magnetic fields then the inflation energy scale is bounded from above as rho_{inf}^{1/4} < 2.5 times 10^{-7}M_{Pl} times (B_{obs}/10^{-15}G)^{-2} in a wide class of inflationary magnetogenesis models, where B_{obs} is the observed strength of cosmic magnetic fields. The tensor-to-scalar ratio is correspondingly constrained as r< 10^{-19} times (B_{obs}/10^{-15}G)^{-8}. Therefore, if the reported strength B_{obs} \geq 10^{-15}G is confirmed and if any signatures of gravitational waves from inflation are detected in the near future, then our result indicates some tensions between inflationary magnetogenesis and observations.

Paper Structure

This paper contains 15 sections, 45 equations.

Table of Contents

  1. Introduction
  2. Observational Constraint on Magnetic Power Spectrum
  3. Four Assumptions
  4. Assumption 1: the form of kinetic term
  5. Assumption 2: Avoidance of strong coupling
  6. Assumption 3: Small back reaction
  7. Assumption 4: Magnetogenesis during inflation
  8. Upper Limit on Inflation Energy Scale
  9. Additional Interaction Terms
  10. Gauge and Lorentz invariant quadratic term
  11. Model with negative interaction energy
  12. Energy conserving term
  13. Energy conserving term
  14. Conclusion
  15. Derivation of the Constraint on Magnetic Power Spectrum