Probing ultralight scalar, vector and tensor dark matter with pulsar timing arrays

Pulsar timing arrays (PTAs) are sensitive to oscillations in the gravitational potential along the line-of-sight due to ultralight particle pressure. We calculate the probing power of PTAs for ultralight bosons across all frequencies, from those larger than the inverse observation time to those smaller than the inverse distance to the pulsar. We show that since the signal amplitude grows comparably to the degradation in PTA sensitivity at frequencies smaller than inverse observation time, the discovery potential can be extended towards lower masses by over three decades, maintaining high precision. We demonstrate that, in the mass range ${10}^{-26}-{10}^{-23}$ eV, existing 15-year PTA data can robustly detect or rule out an ultralight component down to $O\left(1-10\right)\text{%}$ of the total dark matter. Non-detection, together with other bounds in different mass ranges, will imply that ultralight scalar/axion can comprise at most $1-10\text{%}$ of dark matter in the ${10}^{-30}-{10}^{-17}$ eV range. With 30 years of observation, current PTAs can extend the reach down to $0.1-1\text{%}$, while next-generation PTAs such as SKA can attain the $0.01-0.1\text{%}$ precision. We generalize and derive predictions for ultralight spin-1 vector (i.e. dark photon) and spin-2 tensor dark components.