  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.
