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

G. Leonardo Quintanar

Instituto de Física, Universidad Nacional Autónoma de México, Apdo.Postal 20-364, 01000, México D.F., México

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Axel de la Macorra

Instituto de Física, Universidad Nacional Autónoma de México, Apdo.Postal 20-364, 01000, México D.F., México

E-mail Address: macorra@fisica.unam.mx

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https://doi.org/10.1142/S0218271817500043Cited by:0 (Source: Crossref)

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 $g$ $g$ . 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 $g$ $g$ 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 $V_{min} > 0$ $V_{min} > 0$ , the system behaves as a cosmological constant, thus leading eventually to an accelerated universe; (2) if the minimized potential vanishes $V_{min} = 0$ $V_{min} = 0$ , then we have matter with no acceleration; (3) finally a negative minimum $V_{min} < 0$ $V_{min} < 0$ 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.

Keywords:

PACS: 95.36.+x, 98.80.jk

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