A classical cosmological model for triviality

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Abstract

The aim of this paper is to study the triviality of $\lambda\phi^{4}$ theory in a classical gravitational model. Starting from a conformal invariant scalar tensor theory with a self-interaction term $\lambda\phi^{4}$, we investigate the effect of a conformal symmetry breaking emerging from the gravitational coupling of the large-scale distribution of matter in the universe. Taking in this cosmological symmetry breaking phase the infinite limit of the maximal length (the size of the universe) and the zero limit of the minimal length (the Planck length) implies triviality, i.e. a vanishing coupling constant $\lambda$. It suggests that the activity of the self-interaction term $\lambda\phi^{4}$ in the cosmological context implies that the universe is finite and a minimal fundamental length exists.