Subluminal stochastic gravitational waves in pulsar-timing arrays and
  astrometry
  The detection of a stochastic background of low-frequency gravitational waves
by pulsar-timing and astrometric surveys will enable tests of gravitational
theories beyond general relativity. These theories generally permit
gravitational waves with non-Einsteinian polarization modes, which may
propagate slower than the speed of light. We use the total-angular-momentum
wave formalism to derive the angular correlation patterns of observables
relevant for pulsar timing arrays and astrometry that arise from a background
of subluminal gravitational waves with scalar, vector, or tensor polarizations.
We find that the pulsar timing observables for the scalar longitudinal mode,
which diverge with source distance in the luminal limit, are finite in the
subluminal case. Furthermore, we apply our results to $f(R)$ gravity, which
contains a massive scalar degree of freedom in addition to the standard
transverse-traceless modes. The scalar mode in this $f(R)$ theory is a linear
combination of the scalar-longitudinal and scalar-transverse modes, exciting
only the monopole and dipole for pulsar timing arrays and only the dipole for
astrometric surveys.
