  Inflationary and bouncing scenarios are two frameworks that provide the
mechanism to overcome the horizon problem as well as generate the primordial
perturbations. In this work, we investigate the conservation of perturbations
in single-field models of both inflationary and bouncing scenarios, where the
quantity, $z = a \, \rm d \phi/{\rm d}\log a$, with $a$ representing the scale
factor and $\phi$ denoting the scalar field, decreases with time. We observe
that this behaviour occurs during the ultra-slow-roll phase in the context of
inflation and the contracting phase in the context of bounce. We show that the
conjugate momentum associated with the comoving curvature perturbation during
both the ultra-slow-roll phase and the contracting phase of bouncing scenarios
is conserved in the super-Hubble limit. We illustrate that, within the
framework of inflation, this conservation of momentum allows for the evolution
of perturbations across the ultra-slow-roll phase, enabling the calculation of
the power spectrum for modes that exit the Hubble radius before the
ultra-slow-roll phase begins. Similarly, in the context of a bounce, we can
determine the power spectrum after the bounce using this method. We support our
approach with both numerical and analytical arguments.
