Planck-Suppressed Operators

TL;DR

Planck constraints on primordial non-Gaussianity are leveraged to bound high-scale Planck-suppressed couplings between the inflaton and hidden-sector fields. The authors formulate a two-field EFT with a shift-symmetric inflaton Φ and a light hidden field Σ, including mixing up to dimension five, and show that non-Gaussianity arises from hidden-sector self-interactions or nonlinear inflaton–hidden mixing, depending on the regime. They derive lower bounds on the suppression scale Λ—typically Λ > 10^2 H for Gaussian hidden sectors and Λ > 10^5 H when hidden-sector cubic couplings are order H—while noting that a tensor detection (r > 0.01) would push Λ toward the Planck scale. They further connect these results to supersymmetric scenarios, showing how sequestering can yield different signatures and bounds, thereby linking CMB constraints to ultraviolet completions of inflation and gravity.

Abstract

We show that the recent Planck limits on primordial non-Gaussianity impose strong constraints on light hidden sector fields coupled to the inflaton via operators suppressed by a high mass scale Λ. We study a simple effective field theory in which a hidden sector field is coupled to a shift-symmetric inflaton via arbitrary operators up to dimension five. Self-interactions in the hidden sector lead to non-Gaussianity in the curvature perturbations. To be consistent with the Planck limit on local non-Gaussianity, the coupling to any hidden sector with light fields and natural cubic couplings must be suppressed by a very high scale Λ> 10^5 H. Even if the hidden sector has Gaussian correlations, nonlinearities in the mixing with the inflaton still lead to non-Gaussian curvature perturbations. In this case, the non-Gaussianity is of the equilateral or orthogonal type, and the Planck data requires Λ> 10^2 H.

Figures (11)

• Figure 1: The inflaton sector and the hidden sector mix through irrelevant operators suppressed by the scale $\Lambda$.
• Figure 2: Hierarchies of scales in the weak mixing regime.
• Figure 3: Hierarchies of scales in the strong mixing regime. The Hubble scale $H$ may be above or below the scale $M=m^2/\rho$.
• Figure 4: Non-Gaussian phenomenology, for $m=H$. The grey regions correspond to $|f_{\mathsmaller{\rm NL}}| > 10$.
• Figure 5: Feynman diagrams describing the conversion of hidden sector fluctuations $\sigma$ into observable fluctuations $\varphi$ (or $\zeta$).