Generalized ModMax and the Early Universe

TL;DR

This work explores a cosmology driven by Generalized ModMax nonlinear electrodynamics as the energetic source in the early Universe. By deriving the GMM energy density and pressure and treating the primordial magnetic field within a perfect-fluid framework, the authors show that choosing $\sigma<0$ and $\beta<0$ yields a finite energy density near $a\to0$ and an early exponential expansion $a(t) \sim a_{ini} e^{t/\sqrt{3\beta}}$, thereby avoiding the initial singularity. They analyze whether GMM can also drive inflation consistent with Planck constraints, deriving $\eta_{GMM}$ and using $n_s \approx 0.9649$, $r<0.064$, and $50\le N\le 60$ to identify parameter regions; they present explicit examples (e.g., with $\mathcal{F}_{end} \sim 5\times10^{30}$ cm$^{-2}$, $\gamma \approx 270$, $\beta$ of order tens cm$^2$, and $\sigma \sim 10^{-2}$) where the conditions are satisfied. The results indicate that a non-singular Universe with a Planck-consistent inflationary epoch is achievable within Generalized ModMax, though further phenomenology is required to tightly constrain the parameter space and confirm robustness. This work offers an alternative route to early-Universe dynamics that merges nonlinear electrodynamics with cosmology and highlights observable implications tied to primordial magnetic fields.

Abstract

In this work, we study a cosmological model driven by Generalized ModMax nonlinear electrodynamics. We find that, with an appropriate choice of the theory's parameters, the universe's initial singularity can be avoided. Moreover, we also find that this model has an inflationary epoch that is consistent with the current values for $N$, $n_s$ and $r$. Therefore, using Generalized ModMax, we can construct a non singular Universe with an inflationary epoch.

Figures (2)

• Figure 1: In a solid line, the energy density $\rho_\text{GMM}$ as a function of the scale factor $a$ for $\sigma<0$ and $\beta<0$. In a dotted line, the initial value of the energy density, $\rho_0 = \rho_\text{GMM}(a=0)$, as defined in equation \ref{['eq:16']}.
• Figure 2: Scale factor as a function of time at early and late times (boxed figure). The solid line is the asymptotic behavior of $a(t)$ Eq.\ref{['eq:23']} and Eq.\ref{['eq:25']} respectively. The dashed plots are the numerical solutions for Eq.\ref{['eq:21']}, the complete scale factor $a_\text{GMM}(t)$.