Non-Perturbative Yang-Mills Condensate as Dark Energy

Abstract

Models based on Yang-Mills condensate (YMC) have been advocated in the literature and claimed to be successful candidates to explain dark energy. Several instantiations of this simple idea have been considered, the most promising of which are reviewed here. Nevertheless, results previously attained heavily relied on the perturbative approach to the analysis of the effective Yang-Mills action, which is only adequate in the asymptotically-free limit, and were extended into a regime, the infrared limit, in which confinement is expected. We show that if a minimum of the effective Lagrangian in $θ\!=\! - F_{\, \, μν}^a \, F^{a μν}/2$ exists, a YMC forms that drives the Universe toward an accelerated de Sitter phase. The details of the models depend weakly on the specific form of the effective Yang-Mills Lagrangian. Using non-perturbative techniques mutated from the functional renormalization group procedure, we finally show that the minimum in $θ$ of the effective Lagrangian exists, thus YMC can actually take place. The non-perturbative model has properties similar to the ones of the perturbative model. In the early stage of the universe, the YMC equation of state has an evolution that resembles the radiation component, i.e. $w_y \rightarrow 1/3$. However, in the late stage, $w_y$ naturally runs to the critical state with $w_y =-1$, and the universe transits from matter-dominated into dark energy dominated stage only recently, at a redshift the value of which depends on the initial conditions that are chosen while solving the dynamical system.