Doppler boosting the stochastic gravitational wave background
  One of the guaranteed features of the stochastic gravitational wave
background (SGWB) is the presence of Doppler anisotropies induced by the motion
of the detector with respect to the rest frame of the SGWB source. We point out
that kinematic effects can be amplified if the SGWB is characterised by large
tilts in its spectrum as a function of frequency, or by sizeable intrinsic
anisotropies. Hence we examine the possibility to use Doppler effects as
complementary probes of the SGWB frequency profile. For this purpose we work in
multipole space, and we study the effect of kinematic modulation and aberration
on the GW energy density parameter and on its angular power spectrum. We
develop a Fisher forecast analysis and we discuss prospects for constraining
parameters controlling kinematically induced anisotropies with future detector
networks. As a case study, we apply our framework to a background component
with constant slope in frequency, potentially detectable by a network of future
ground-based interferometers. For this specific example, we show that a
measurement of kinematic anisotropies with a network of Einstein Telescope and
Cosmic Explorer will allow us to constrain the spectral shape with a precision
of about 16$\%$. Finally, we identify cosmological and astrophysical scenarios
where kinematic effects are enhanced in frequency ranges probed by current and
future GW experiments.
