  In this work, we present a quintessential interpretation of having a
blue-tilted tensor power spectrum for canonical single-field slow-roll
inflation to explain the recently observed Pulsar Timing Array (NANOGrav
15-year and EPTA) signal of Gravitational Waves (GW). We formulate the complete
semi-classical description of cosmological perturbation theory in terms of
scalar and tensor modes using the Non-Bunch Davies initial condition. We found
that the existence of the blue tilt ($n_t$) within the favoured range
$1.2<n_t<2.5$ can be explained in terms of a newly derived consistency
relation. Further, we compute a new field excursion formula using the Non-Bunch
Davies initial condition, that validates the requirement of Effective Field
Theory in the sub-Planckian regime, $|\Delta\phi|\ll M_{\rm pl}$ for the
allowed value of the tensor-to-scalar ratio, $r<0.06$ from CMB observations. In
our study, we refer to this result as Anti Lyth bound as it violates the
well-known Lyth bound originally derived for Bunch Davies initial condition.
Further, we study the behaviour of the spectral density of GW and the
associated abundance with the frequency, which shows that within the frequency
domain $10^{-9}{\rm Hz}<f<10^{-7}{\rm Hz}$ the outcome obtained from our
analysis is completely consistent with the Pulsar Timing Array (NANOGrav
15-year and EPTA) signal. Also, we found that the behaviour of GW spectra
satisfies the CMB constraints 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 frequency domain $10^{-7}{\rm Hz}<f<1{\rm Hz}$ validates our theory
in the comparatively high-frequency regime as well.
