  Pure $R^2$ gravity has been shown to be equivalent to Einstein gravity with
non-zero cosmological constant and a massless scalar field. We show that the
Palatini formulation of pure $R^2$ gravity is equivalent to Einstein gravity
with non-zero cosmological constant as before but with no massless scalar
field. This is an important new development because the massless scalar field
is not readily identifiable with any known particle in nature or unknown
particles like cold dark matter which are expected to be massive. We then
include a non-minimally coupled Higgs field as well as fermions to discuss how
the rest of the standard model fields fit into this paradigm. With Higgs field,
Weyl invariance is maintained by using a hybrid formalism that includes both
the Palatini curvature scalar $\mathcal{R}$ and the usual Ricci scalar $R$
