  Conformal higher spin (CHS) field theory, which is a solid part of recent
advanced checks of AdS/CFT correspondence, finds applications in cosmology.
Hidden sector of weakly interacting CHS fields suggests a resolution of the
hierarchy problem in the model of initial conditions for inflationary cosmology
driven by a conformal field theory. These initial conditions are set by thermal
garland type cosmological instantons in the sub-planckian energy range for the
model of CHS fields with a large positive coefficient $\beta$ of the
Gauss-Bonnet term in their total conformal anomaly and a large number of their
polarizations $\mathbb{N}$. The upper bound of this range $M_P/\sqrt\beta$ is
shown to be much lower than the gravitational cutoff $M_P/\sqrt\mathbb{N}$
which is defined by the requirement of smallness of the perturbatively
nonrenormalizable graviton loop contributions. In this way we justify the
approximation scheme in which the nonrenormalizable graviton sector is subject
to effective field theory under this cutoff, whereas the renormalizable sector
of multiple CHS fields is treated beyond perturbation theory and dynamically
generates the bound on the inflation scale of the CFT cosmology
$M_P/\sqrt\beta\ll M_P/\sqrt\mathbb{N}$. This confirms recent predictions for
the origin of the Starobinsky $R^2$ and Higgs inflation models from the CHS
cosmology, which occurs at the energy scale three or four orders of magnitude
below the gravitational cutoff, $\sqrt{\mathbb{N}/\beta}\sim 10^{-3}\div
10^{-4}$. We also consider cosmological models dominated by fermionic CHS
fields with a negative $\beta$ and anomaly free models of infinite towers of
CHS fields with $\beta=0$ and briefly discuss the status of unitarity in CHS
models.
