Generic 3-point statistics with tensor modes in light of Swampland and Trans-Planckian Censorship Conjecture

Abstract

Abstract Recently proposed Swampland Criteria (SC) and Trans-Planckian Censorship Conjecture (TCC) question the theoretical consistency of inflationary cosmology. While SC can be in tension with the recent observational bound on tensor-to-scalar ratio which is a consequence of single field consistency relation, the requirement of TCC translates to the fact that inflation can not produce a detectable signal for stochastic gravitational wave, raising a question on future prospects of detection of Primordial Gravitational Waves (PGW). But the constraint can be relaxed significantly by considering Non Bunch Davies (NBD) initial states, that in turn brings back the observational relevance of PGW via its 2-point function. Also with NBD states the tension between SC and observational bound on tensor-to-scalar ratio vanishes. Focusing on these theoretical importance of NBD states, in this article we develop consistent 3-point statistics with tensor modes for all possible correlators (auto and mixed) for NBD initial states in a generic, model independent framework of Effective Field Theory of inflation and analyze the properties of the correlators in the light of TCC. We also construct the templates of the corresponding nonlinearity parameters $$f_{NL}$$ f NL for different shapes of relevance and investigate if any of the 3-point correlators could be of interest for future CMB missions. Our analysis reveals that the prospects of detecting the tensor auto correlator are almost nil whereas the mixed correlators might be relevant for future CMB missions.