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How to obtain slow roll inflation driven by non-linear electrodynamics

Daniele Malafarina, Hrishikesh Chakrabarty, Ilia Musco

TL;DR

This work investigates whether slow-roll inflation can be driven by non-linear electrodynamics in a magnetic universe within General Relativity. By deriving slow-roll conditions in terms of the NLED Lagrangian, it shows that many previously proposed models fail to satisfy both $\epsilon \ll 1$ and $\eta \ll 1$ simultaneously and hence cannot yield viable inflation. The authors identify a Maxwell-limit Lagrangian class, $\mathcal{L} = -\alpha \log \big(1 + \beta F + h(F)\big)$, with the simplest case $h(F)=0$ providing controlled slow-roll behavior and a natural end to inflation near $\beta F \approx 3.9$, while preserving the correct weak-field Maxwell limit. They also discuss residual issues, including perturbations and quantum consistency, requiring further work to firmly connect to observations. Overall, the paper delineates rigorous slow-roll criteria for NLED-driven inflation and presents a concrete, Maxwell-consistent model as a viable path forward, pending further observational and quantum analyses.

Abstract

We establish for the first time the conditions that must be imposed on the action for a magnetic universe in a theory of non-linear electrodynamics in order to have an asymptotically de Sitter initial state followed by a slow roll inflationary phase. We show that models so far proposed in the literature do not allow for a prolonged inflationary phase consistent with observations. We construct a Lagrangian that reduces to the Maxwell one in weak field; this is the only class of models that satisfies the required conditions for slow roll in the early Universe.

How to obtain slow roll inflation driven by non-linear electrodynamics

TL;DR

This work investigates whether slow-roll inflation can be driven by non-linear electrodynamics in a magnetic universe within General Relativity. By deriving slow-roll conditions in terms of the NLED Lagrangian, it shows that many previously proposed models fail to satisfy both and simultaneously and hence cannot yield viable inflation. The authors identify a Maxwell-limit Lagrangian class, , with the simplest case providing controlled slow-roll behavior and a natural end to inflation near , while preserving the correct weak-field Maxwell limit. They also discuss residual issues, including perturbations and quantum consistency, requiring further work to firmly connect to observations. Overall, the paper delineates rigorous slow-roll criteria for NLED-driven inflation and presents a concrete, Maxwell-consistent model as a viable path forward, pending further observational and quantum analyses.

Abstract

We establish for the first time the conditions that must be imposed on the action for a magnetic universe in a theory of non-linear electrodynamics in order to have an asymptotically de Sitter initial state followed by a slow roll inflationary phase. We show that models so far proposed in the literature do not allow for a prolonged inflationary phase consistent with observations. We construct a Lagrangian that reduces to the Maxwell one in weak field; this is the only class of models that satisfies the required conditions for slow roll in the early Universe.

Paper Structure

This paper contains 5 sections, 34 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Evolution of a magnetic universe
  3. Conditions for slow roll inflation
  4. Magnetic Universe with slow roll inflation
  5. Discussion

Figures (1)

  • Figure 1: Left: Comparison of the time evolution of the scale factor $a$ between a magnetic universe dominated by the nonlinear electrodynamics Lagrangian as in Eq. \ref{['our']} (solid line) and a radiation dominated universe (dashed line). The values of $\beta = 10^{-3}$ and the strength of the magnetic field today $B_0 = 2$, are chosen for illustrative purposes. Right: Evolution of the slow-roll parameters with respect to $\beta F$ for the Lagrangian in Eq. \ref{['our']} (notice that $\beta F$ grows as $t$ goes to minus infinity). In the early universe, i.e. for $\beta F$ large, both parameters go to zero. the vertical dotted line represents the end of inflation.