  We calculate six invariant terms of a gravitational field theory that
nonlinearly realizes the Conformal/Poincar\'e quotient, and reduce to the known
conformal Galileons in the limit when only the conformal mode is kept. Five of
the six terms are regular coset terms, while the sixth is a Wess-Zumino (WZ)
term that gives the well-known gravitational action for the trace anomaly. The
obtained terms can be embedded in a quantum effective field theory (EFT)
without spoiling their key features, although at a cost of certain fine
tunings. The additional massive modes that appear in the EFT would have been
troublesome, however, for sub-Planckian curvatures their masses are
(super)-Planckian and therefore the respective states are outside of the EFT
regime. We discuss certain novel cosmological solution of this theory and their
validity within the EFT. Furthermore, we show that the obtained 4D terms,
except the WZ term, can also be derived from higher dimensional Lovelock terms
by reducing the latter to the genuinely four dimensional terms according to a
well-defined algorithm.
