Cosmological implications of Nambu–Jona-Lasinio model with a dynamical coupling

Abstract

We study the cosmological implications of the Nambu–Jona-Lasinio (NJL) model when the coupling constant is field dependent. The NJL model has a four-fermion interaction describing two different phases due to quantum interaction effects and determined by the strength of the coupling constant [Formula: see text]. It describes massless fermions for weak coupling and a massive fermions and strong coupling, where a fermion condensate is formed. In the original NJL model, the coupling constant [Formula: see text] is indeed constant, and in this work we consider a modified version of the NJL model by introducing a dynamical field dependent coupling motivated by string theory. The effective potential as a function of the varying coupling (aimed to implement a natural phase transition) is seen to develop a negative divergence, i.e. becomes a “bottomless well” in certain limit region. Although we explain how an lower unbounded potential is not necessarily unacceptable in a cosmological context, the divergence can be removed if we consider a mass term for the coupling like field. We found that for a proper set of parameters, the total potential obtained has two minima, one located at the origin (the trivial solution, in which the fluid associated with the fields behave like matter); and the other related to the nontrivial solution. This last solution has three possibilities: (1) if the minimum is positive [Formula: see text], the system behaves as a cosmological constant, thus leading eventually to an accelerated universe; (2) if the minimized potential vanishes [Formula: see text], then we have matter with no acceleration; (3) finally a negative minimum [Formula: see text] leads an eventually collapsing universe with a flat geometry. Therefore, a possible interpretation as dark matter (DM) or dark energy (DE) is allowed among the behaviors implicated in the model.