  We quantitatively study how the primordial density fluctuations are imprinted
on the anisotropy of the phase transition gravitational wave (PTGW). Generated
long before recombination and free from Silk damping, the anisotropic PTGW
might reveal the density perturbation seeded from inflation or alternatives. We
find new behaviors of the PTGW anisotropy power spectrum. The PTGW anisotropy
is stronger than the anisotropy of the cosmic microwave background temperature
at all scales, and the high-$\ell$ multiples are enhanced about 1 order due to
the early integrated Sachs-Wolfe effect. Furthermore, differences in primordial
power spectra at small scales manifest themselves more significantly on the
angular power spectrum of PTGW anisotropy compared to that of the cosmic
microwave background. These properties might provide a novel clue to
understanding the primordial density perturbation of our early Universe and
thereby complete our understanding of inflation theory. Taking nanohertz PTGW
from dark matter models as a typical example, we obtain amplitudes of PTGW
anisotropy which are about 4 or 3 orders weaker than the isotropic PTGW energy
spectra.
