  Pulsar timing array (PTA) collaborations in North America, Australia, and
Europe, have been exploiting the exquisite timing precision of millisecond
pulsars over decades of observations to search for correlated timing deviations
induced by gravitational waves (GWs). PTAs are sensitive to the frequency band
ranging just below 1 nanohertz to a few tens of microhertz. The discovery space
of this band is potentially rich with populations of inspiraling supermassive
black-holes binaries, decaying cosmic string networks, relic post-inflation
GWs, and even non-GW imprints of axionic dark matter. This article aims to
provide an understanding of the exciting open science questions in cosmology,
galaxy evolution, and fundamental physics that will be addressed by the
detection and study of GWs through PTAs. The focus of the article is on
providing an understanding of the mechanisms by which PTAs can address specific
questions in these fields, and to outline some of the subtleties and
difficulties in each case. The material included is weighted most heavily
towards the questions which we expect will be answered in the near-term with
PTAs; however, we have made efforts to include most currently anticipated
applications of nanohertz GWs.
