  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.
