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Primordial inflation may represent the most powerful collider to testhigh-energy physics models. In this paper we study the impact on theinflationary power spectrum of the comoving curvature perturbation in thespecific model where massive higher spin fields are rendered effectivelymassless during a de Sitter epoch through suitable couplings to the inflatonfield. In particular, we show that such fields with spin $s$ induce adistinctive statistical anisotropic signal on the power spectrum, in such a waythat not only the usual $g_{2M}$-statistical anisotropy coefficients, but alsohigher-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 cosmicmicrowave background and galaxy power spectra. Our Fisher matrix forecastsindicate that the detectability of $g_{LM}$ depends very weakly on $L$: allcoefficients could be detected in near future if their magnitudes are biggerthan about $10^{-3}$.

Detecting higher spin fields through statistical anisotropy in the CMB and galaxy power spectra