  We study a scenario based upon a mass-less $\lambda \phi^4$ theory coupled to
massive neutrino matter with $Z_2$ symmetry using a conformal coupling,
$A(\phi)=1-\alpha\phi^2/2M_{pl}^2;~\alpha=M^2_{pl}/M^2$ where $M$ is a cut off
mass. The chosen coupling generically leads to the spontaneous symmetry
breaking at late times such that the field acquires non-zero mass,
$m_\phi=(\alpha \Omega_{0\nu})^{1/2}H_0 \ll H_0 $ and rolls slowly around the
true ground state which emerges after spontaneous symmetry breaking. For the
statistical analysis, we utilize Pantheon+Multi-Cycle Treasury and OHD data
sets. We find that even a small fraction of the neutrino matter density
together with its coupling to the scalar field can actually make our model to
behave like a weakly dynamical dark energy and have $\Lambda$CDM model as a
limiting case.
