Anisotropy of phase transition gravitational wave to probe small-scale density perturbation.

We study the anisotropy of phase transition gravitational wave (PTGW) and find it could be a new approach to probe the primordial density perturbation, especially at small scale. Generated long before recombination and free from Silk damping, PTGW could directly provide the information of density perturbation seeded from inflation or alternatives. The power spectrum of anisotropic PTGW even goes up at high $\ell$ due to the early integrated Sachs Wolfe effect, making it a powerful probe into these small scale perturbations. Moreover, we find anisotropic PTGW around nano Hertz could be detected by pulsar timing array projects like the Square Kilometre Array.