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In this work, we present a quintessential interpretation of having ablue-tilted tensor power spectrum for canonical single-field slow-rollinflation to explain the recently observed NANOGracv 15-year signal ofGravitational Waves (GW). We formulate the complete semi-classical descriptionof cosmological perturbation theory in terms of scalar and tensor modes usingthe Non-Bunch Davies initial condition. We found that the existence of the bluetilt ($n_t$) within the favoured range $1.2<n_t<2.5$ can be explained in termsof a newly derived consistency relation. Further, we compute a new fieldexcursion formula using the Non-Bunch Davies initial condition, that validatesthe requirement of Effective Field Theory in the sub-Planckian regime,$|\Delta\phi|\ll M_{\rm pl}$ for the allowed value of the tensor-to-scalarratio, $r<0.06$ from CMB observations. In our study, we refer to this result asAnti Lyth bound as it violates the well-known Lyth bound originally derived forBunch Davies initial condition. Further, we study the behaviour of the spectraldensity of GW and the associated abundance with the frequency, which shows thatwithin the frequency domain $10^{-9}{\rm Hz}<f<10^{-7}{\rm Hz}$ the outcomeobtained from our analysis is completely consistent with the NANOGracv 15-yearsignal. Also, we found that the behaviour of GW spectra satisfies the CMBconstraints at the low frequency, $f_*\sim 7.7\times 10^{-17}{\rm Hz}$corresponding to the pivots scale wave number, $k_*\sim 0.05{\rm Mpc}^{-1}$.Finally, the sharp falling behaviour of the GW spectra within the frequencydomain $10^{-7}{\rm Hz}<f<1{\rm Hz}$ validates our theory in the comparativelyhigh-frequency regime as well.

Single field inflation in the light of NANOGrav 15-year Data:  Quintessential interpretation of blue tilted tensor spectrum through  Non-Bunch Davies initial condition