Scalar Stochastic Gravitational-Wave Background in Brans-Dicke Theory of
  Gravity
  We study the scalar stochastic gravitational-wave background (SGWB) from
astrophysical sources, including compact binary mergers and stellar collapses,
in the Bras-Dicke theory of gravity. By contrast to tensor waves, we found the
scalar SGWB to predominantly arise from stellar collapses. These collapses not
only take place at higher astrophysical rates, but emit more energy. This is
because, unlike tensor radiation, which mainly starts from quadrupole order,
the scalar perturbation can be excited by changes in the monopole moment. In
particular, in the case of stellar collapse into a neutron star or a black
hole, the monopole radiation, at frequencies below 100\,Hz, is dominated by the
memory effect. At low frequencies, the scalar SGWB spectrum follows a power law
of $\Omega_\text{S}\propto f^\alpha$, with $\alpha = 1$. We predict that
$\Omega_\text{S}$ is inversely proportional to the square of $\omega_{\rm
BD}+2$, with $\quad(\omega_{\rm BD}+2)^2\Omega_S(f=25\,{\rm Hz}) = 2.8\times
10^{-6}$. We also estimate the detectability of the scalar SGWB for current and
third-generation detector networks, and the bound on $\omega_{\rm BD}$ that can
be imposed from these observations.
