Heavy Particle Signatures in Cosmological Correlation Functions with Tensor Modes

We explore the possibility to make use of cosmological data to look for signatures of unknown heavy particles whose masses are on the order of the Hubble parameter during the time of inflation. To be more specific we take up the quasi-single field inflation model, in which the isocurvaton $\sigma $ is supposed to be the heavy particle. We study correlation functions involving both scalar ($\zeta $) and tensor ($\gamma $) perturbations and search for imprints of the $\sigma$-particle effects. We make use of the technique of the effective field theory for inflation to derive the $\zeta \sigma $ and $\gamma \zeta \sigma $ couplings. With these couplings we compute the effects due to $\sigma $ to the power spectrum $\langle \zeta \zeta \rangle $ and correlations $\langle \gamma^{s} \zeta \zeta \rangle$ and $\langle \gamma^{s_{1}} \gamma ^{s_{2}} \zeta \zeta \rangle $, where $s$, $s_{1}$ and $s_{2}$ are the polarization indices of gravitons. Numerical analyses of the $\sigma$-mass effects to these corrlations are presented. It is argued that future precise observations of these correlations could make it possible to measure the $\sigma$-mass and the strength of the $\zeta \sigma$ and $\gamma \zeta \sigma$ couplings. As an extension to the $N$-graviton case we also compute the correlations $\langle \gamma ^{s_{1}} \cdots \gamma ^{s_{N}} \zeta \zeta \rangle $ and $\langle \gamma ^{s_{1}} \cdots \cdots \gamma ^{s_{2N}} \zeta \zeta \rangle $ and their $\sigma$-mass effects. It is suggested that larger $N$ correlation functions are useful to probe larger $\sigma$-mass .