Probing the inflationary particle content: extra spin-2 field

We study how inflationary observables associated with primordial tensor modes are affected by coupling the minimal field content with an extra spin-2 particle during inflation. We work with a model that is ghost-free at the fully non-linear level and show how the new degrees of freedom modify standard consistency relations for the tensor bispectrum. The extra interacting spin-2 field is necessarily massive and unitarity dictates its mass be in the $m \gtrsim H$ range. Despite the fact that this bound selects a decaying solution for the corresponding tensor mode, cosmological correlators still carry the imprints of such "fossil" fields. Remarkably, fossil(s) of spin $\geq 1$ generate distinctive anisotropies in observables such as the tensor power spectrum. We show how this plays out in our set-up.Comment: 25 pages, 3 figure