  Primordial inflation may represent the most powerful collider to test
high-energy physics models. In this paper we study the impact on the
inflationary power spectrum of the comoving curvature perturbation in the
specific model where massive higher spin fields are rendered effectively
massless during a de Sitter epoch through suitable couplings to the inflaton
field. In particular, we show that such fields with spin $s$ induce a
distinctive statistical anisotropic signal on the power spectrum, in such a way
that not only the usual $g_{2M}$-statistical anisotropy coefficients, but also
higher-order ones (i.e., $g_{4M}$, $g_{6M}$, $\cdots$, $g_{(2s-2)M}$ and
$g_{(2s) M}$) are nonvanishing. We examine their imprints in the cosmic
microwave background and galaxy power spectra. Our Fisher matrix forecasts
indicate that the detectability of $g_{LM}$ depends very weakly on $L$: all
coefficients could be detected in near future if their magnitudes are bigger
than about $10^{-3}$.
