Search for sub-solar mass binaries with Einstein Telescope and Cosmic
  Explorer
  A possible detection of sub-solar mass ultra-compact objects would lead to
new perspectives on the existence of black holes that are not of astrophysical
origin and/or pertain to formation scenarios of exotic ultra-compact objects.
Both possibilities open new perspectives for better understanding of our
universe. In this work, we investigate the significance of detection of
sub-solar mass binaries with components mass in the range: $10^{-2} M_\odot$ up
to 1$M_\odot$, within the expected sensitivity of the ground-based
gravitational waves detectors of third-generation, viz., the Einstein Telescope
(ET) and the Cosmic Explorer (CE). Assuming a minimum of amplitude
signal-to-noise ratio for detection, viz., $\rho = 8$, we find that the maximum
horizon distances for an ultra-compact binary system with components mass
$10^{-2} \, M_\odot$ and 1$M_\odot$ are 40 Mpc and 1.89 Gpc, respectively, for
ET, and 125 Mpc and 5.8 Gpc, respectively, for CE. Other cases are also
presented in the text. We derive the merger rate, and discuss consequences on
the abundances of primordial black hole (PBH), $f_{\rm PBH}$. Considering the
entire mass range [$10^{-2}$ - 1]$M_\odot$, we find $f_{\rm PBH} < 0.70$ ($<$
$0.06$) for ET (CE), respectively.
