Dynamical symmetry breaking and negative cosmological constant

In the context of Clifford functional integral formalism, we revisit the Nambu–Jona-Lasinio-type dynamical symmetry breaking model and examine the properties of the dynamically generated composite bosons. Given that the model with 4-fermion interactions is nonrenormalizable in the traditional sense, the aim is to gain insight into the divergent integrals without resorting to explicit regularization. We impose a restriction on the linearly divergent primitive integrals, thus resolving the long-standing issue of momentum routing ambiguity associated with fermion–antifermion condensations. The removal of the ambiguity paves the way for the possible calculation of the true ratio of Higgs boson mass to top quark mass in the top condensation model. In this paper, we also investigate the negative vacuum energy resulted from dynamical symmetry breaking and its cosmological implications. In the framework of modified Einstein–Cartan gravity, it is demonstrated that the late-time acceleration is driven by a novel way of embedding the Hubble parameter into the Friedmann equation via an interpolation function, whereas the dynamically generated negative cosmological constant only plays a minor role for the current epoch. Two cosmic scenarios are proposed, with one of which suggesting that the universe may have been evolving from an everlasting coasting state towards the accelerating era characterized by the deceleration parameter approaching −0.5 at low redshift. One inevitable outcome of the modified Friedmannian cosmology is that the directly measured local Hubble parameter should in general be larger than the Hubble parameter calibrated from the conventional Friedmann equation. This Hubble tension becomes more pronounced when the Hubble parameter is comparable or less than a characteristic Hubble scale.