Pulsar-timing arrays, astrometry, and gravitational waves
  We discuss the theory of pulsar-timing and astrometry probes of a stochastic
gravitational-wave background with a recently developed
"total-angular-momentum" (TAM) formalism for cosmological perturbations. We
review the formalism, emphasizing in particular the features relevant for this
work and describe the observables we consider (i.e. the pulsar redshift and
stellar angular displacement). Using the TAM approach, we calculate the angular
power spectra for the observables and from them derive angular auto- and
cross-correlation functions. We provide the full set of power spectra and
correlation functions not only for the standard transverse-traceless
propagating degrees of freedom in general relativity, but also for the four
additional non-Einsteinian polarizations that may arise in alternative-gravity
theories. We discuss how pulsar-timing and astrometry surveys can complement
and serve as cross checks to one another and comment on the importance of
testing the chirality of the gravitational-wave background as a tool to
understand the nature of its sources. A simple rederivation of the power
spectra from the plane-wave formalism is provided in an Appendix.
