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We attempt a novel mechanism to understand the underlying cause of late-timecosmic acceleration using a distinguished physical process taking place in thelate Universe. The turning of massive neutrinos from relativistic tonon-relativistic might cause a phase transition at late times. We implementthis idea using massless $\lambda \phi^4$ theory coupled to massive neutrinomatter such that the coupling is proportional to the trace of theenergy-momentum tensor of neutrino matter. As massive neutrinos becomenon-relativistic, their coupling to the scalar field builds up dynamicallygiving rise to spontaneous symmetry breaking in the low-density regime. As aresult, in the true vacuum, the field acquires non zero mass proportional tothe energy density of massive neutrino matter and could give rise to late-timecosmic acceleration. We also address the issues related to stability of selfcoupling under radiative corrections.

Can massive neutrinos be responsible for late time phase transition $\hat{\rm a}$ {\it la} deceleration to acceleration in our Universe?