  Recently proposed Swampland Criteria (SC) and Trans-Planckian Censorship
Conjecture (TCC) together put stringent theoretical constraints on slow roll
inflation, raising a question on future prospects of detection of Primordial
Gravitational Waves (PGW). As it appears, the only option to relax the
constraints is by considering Non Bunch Davies (NBD) initial states, that in
turn brings back the observational relevance of PGW via its 2-point function.
In this article we develop consistent 3-point statistics with tensor modes for
all possible correlators (auto and mixed) for NBD initial states in the light
of SC and TCC in a generic, model independent framework of Effective Field
Theory of inflation. We also construct the templates of the corresponding
nonlinearity parameters $f_{NL}$ 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.
