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

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 ${10}^{-3}$.