  In the general frameworks of an earlier introduced
quartet-metric/multi-component gravity, a theory of a massive scalar graviton
supplementing the massless tensor one is consistently deduced. The
peculiarities of the scalar-graviton field compared to the canonical scalar one
are demonstrated. The light scalar graviton is treated as an emergent dark
substance of the Universe: dark matter and/or dark energy depending on the
solution. The case with scalar graviton as dark energy responsible for the
late-time accelerated expansion of the Universe is studied in more detail. In
particular, it is shown that due to an attractor solution for the light scalar
graviton there naturally emerges at the classical level a tiny nonzero
effective cosmological constant, even in the absence of the Lagrangian one. The
prospects of going beyond LCDM model per scalar graviton are shortly indicated.
