Non-Abelian $S$-term dark energy and inflation

TL;DR

This paper investigates how a generalized SU(2) Proca theory with a symmetric gauge field tensor influences dark energy and inflation, revealing a dynamical mechanism for accelerated expansion and a slow-roll inflation scenario sensitive to initial conditions.

Contribution

It introduces a novel model involving a cosmic triad in generalized SU(2) Proca theory that explains dark energy and inflation with unique dynamical properties.

Findings

Dark energy behaves as negative and positive energy densities leading to accelerated expansion.

A slow-roll inflationary phase can be sustained by the S term in the model.

The model may evade constraints from gravitational wave observations.

Abstract

We study the role that a cosmic triad in the generalized $SU(2)$ Proca theory, specifically in one of the pieces of the Lagrangian that involves the symmetric version $S_{\mu \nu}$ of the gauge field strength tensor $F_{\mu \nu}$, has on dark energy and primordial inflation. Regarding dark energy, the triad behaves asymptotically as a couple of radiation perfect fluids whose energy densities are negative for the $S$ term but positive for the Yang-Mills term. This leads to an interesting dynamical fine-tuning mechanism that gives rise to a combined equation of state parameter $\omega \simeq -1$ and, therefore, to an eternal period of accelerated isotropic expansion for an ample spectrum of initial conditions. Regarding primordial inflation, one of the critical points of the associated dynamical system can describe a prolonged period of isotropic slow-roll inflation sustained by the $S$ term. This period ends up when the Yang-Mills term dominates the energy density leading to the radiation dominated epoch. Unfortunately, in contrast to the dark energy case, the primordial inflation scenario is strongly sensitive to the coupling constants and initial conditions. The whole model, including the other pieces of the Lagrangian that involve $S_{\mu \nu}$, might evade the recent strong constraints coming from the gravitational wave signal GW170817 and its electromagnetic counterpart GRB 170817A.