  Understanding the nature of primordial fluctuations is critical to our
comprehension of the Universe's early stages. While these fluctuations are
known to be nearly scale-invariant, quasi-adiabatic, and nearly Gaussian on
large scales, their behavior at smaller scales remains less well-defined and
may offer insights into new physics. Recent observations by the NANOGrav, PPTA,
EPTA, and CPTA collaborations suggest the presence of a stochastic
gravitational wave background, which, while consistent with the contribution
from supermassive black hole binaries, also opens the possibility of probing
new physics. This paper explores whether this signal could stem from primordial
isocurvature and adiabatic fluctuations. We adopt parameterized spectra for
both types of fluctuations to fit the observations from the latest NANOGrav
data. Furthermore, we employ Bayesian analysis to assess the distinguishability
of these models in light of current PTA sensitivities. Our findings indicate
that with the capabilities, PTAs cannot conclusively differentiate between
isocurvature and adiabatic fluctuations.
