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We study the polarizations induced by the Galileon as a stochasticgravitational wave background in the cross correlated power in a pulsar timingarray. Working within Galileon gravity, we first show that the scalargravitational wave signature of the Galileon is encoded solely in its effectivemass, which is controlled by the bare mass, conformal coupling, and a tadpole.Then, we study the phenomenology of the Galileon induced scalar polarizationsand place observational constraints on these using the present NANOGrav dataset. Our results feature longitudinal spatial correlation, indicative of a$10^{-22}$ eV {subluminal} Galileon, and show the Galileon polarizations as astatistically compelling source of the observed spatial correlation acrossmillisecond pulsars, if there is any.

Looking out for the Galileon in the nanohertz gravitational wave sky