Possible Signatures of Inflationary Particle Content: Spin-2 Fields

TL;DR

The paper analyzes how a ghost-free massive spin-2 field coupled via dRGT bigravity to the inflaton sector modifies inflationary consistency relations, focusing on the tensor-scalar-scalar squeezed bispectrum. The Higuchi bound enforces a mass of order the Hubble scale, imparting a decaying tensor component and suppressing observable signals, despite two routes to CR breaking and potential loop-induced effects from cubic interactions. The main finding is that, in the studied parameter regime (notably $r_{fg} \ll 1$), the non-standard CRs yield a squeezed-limit amplitude too small to be detected by upcoming surveys, though local quadrupole signatures can remain compatible with current constraints. The work highlights how unitarity bounds and screening mechanisms shape the inflationary imprint of extra spin-2 degrees of freedom and suggests exploring non-minimal couplings or higher-spin extensions for potentially observable effects.

Abstract

We study the imprints of a massive spin-2 field on inflationary observables, and in particular on the breaking of consistency relations. In this setup, the minimal inflationary field content interacts with the massive spin-2 field through dRGT interactions, thus guaranteeing the absence of Boulware-Deser ghostly degrees of freedom. The unitarity requirement on spinning particles, known as Higuchi bound, plays a crucial role for the size of the observable signal.

Figures (6)

• Figure 1: Left: the LHS of Eq. (\ref{['ghiguchi']}) as a function of the physical $k$ for $\mathcal{M}=0$. One can notice that a $k_{\rm ph} \geq \sqrt{8} H$ is enough for a positive $B_{H}$, regardless of the value of $\mathcal{M}$. Right: the LHS of Eq. (\ref{['ghiguchi']}) as a function of the physical $k$ for $\mathcal{M}\sim \sqrt{2}$; for small $k$ the value of $\mathcal{M}$ needs to surpass this threshold in order for the Higuchi bound to be satisfied.
• Figure 2: Diagrammatic representation of a typical 1-loop interaction: -- the left vertex should be thought of as originating from a "new" $m^2M^2$-type interaction; -- the right vertex stems from standard-type direct minimal coupling of $f$ with matter. The black (blue) wiggly line represents $\gamma_g$($\gamma_f$), the solid ones stand for $\zeta$.
• Figure 3: Diagrammatic representation of the quadratic $\gamma_g$-$\gamma_f$ interaction.
• Figure 4: Diagrammatic representation non standard CRs condition.
• Figure 5: Left: contribution to $\langle \gamma_g \zeta \zeta \rangle$ consisting of two "quadratic" $\gamma_g-\gamma_f$ vertices and the usual tree-level tensor-scalar-scalar interaction. Right: A $\gamma_g-\gamma_f$ vertex and a three-vertex which is there only if $\gamma_f$ couples directly with $\zeta$.