Primordial black holes and gravitational waves in nonstandard
  cosmologies
  For primordial black holes (PBHs) to form a considerable fraction of cold
dark matter, the required amplitude of primordial scalar perturbations is quite
large ($P_{\zeta}(k) \sim 10^{-2}$) if PBH is formed in radiation epoch. In
alternate cosmological histories, where additional epoch of arbitrary equation
of state precede radiation epoch, the dynamics of PBH formation and relevant
mass ranges can be different leading to lower requirement of primordial power
at smaller scales of inflation. Moreover, this alternate history can modify the
predictions for the gravitational wave (GW) spectrum, which can be probed by
upcoming GW observations. In this paper, we show that an early kination epoch
can lead to per cent level abundance ofPBH for a lower amplitude of
$P_{\zeta}(k)$ compared to PBH formation in a standard radiation epoch.
Moreover, we calculate the effect of early kination epoch on the GW spectrum
for first and second orders in perturbation theory which show enhancement in
the amplitude of the GW spectrum in a kination epoch with respect to that in a
standard radiation epoch.
