  The standard model is a remarkably consistent and complete quantum field
theory but its coupling to gravity and the Higgs field remain problematic, as
reflected in the cosmological constant problem, the Weyl anomaly, and the
hierarchy puzzle. We point out that 36 conformally-coupled dimension-zero
scalar fields can simultaneously cancel the vacuum energy and both terms in the
Weyl anomaly, if the Higgs field is emergent. The cancellation is highly
non-trivial: given the standard model gauge group $SU(3)\times SU(2)\times
U(1)$, it requires precisely $48$ Weyl fermions, {\it i.e.}, three generations
of standard model fermions, including right-handed neutrinos. Due to a large
additional gauge symmetry, the new scalars contribute no new local degrees of
freedom or particle states. Their only physical state is their vacuum state, in
which they possess a scale invariant power spectrum extending to long
wavelengths. This suggests a new explanation for the primordial scalar
perturbations in cosmology, not requiring inflation. We also discuss how the
Higgs field might emerge as a composite object.
