  Scalar fields with an energy density dominated by its kinetic part may have
played a relevant role in the very early stages of the Universe. Compared to
the standard inflationary paradigm, they may lead to modifications in
observable quantities, e.g. the anisotropies found in the cosmic microwave
background. Kinetically dominated regimes arise in classical fast-roll
scenarios as well as in quantum bouncing cosmologies. For instance, kinetic
dominance is typical in interesting preinflationary phases of Loop Quantum
Cosmology. In this work, we analyze the leading-order effects that the presence
of a scalar field potential causes on the primordial cosmological perturbations
in these kinetically dominated epochs. These effects can be grouped in two
sets, namely, those that affect the effective mass of the perturbations and
those that affect the choice of their vacuum state. The effective mass is
modified directly by terms that include the potential, but also indirectly by
the change in the background dynamics and the relation between the
parameterization of these dynamics and the conformal time, usually employed to
describe the evolution of the perturbations. On the other hand, away from de
Sitter inflation, the Bunch-Davies state is no longer the most natural vacuum
at all scales. Recent proposals suggest to modify it by carrying out certain
Hamiltonian diagonalization with a suitable asymptotic behavior at large
wavenumber scales. Both this diagonalization condition and the imposed
asymptotic behavior depend on the effective mass of the perturbations, and
therefore the selected vacuum state varies in the presence of the scalar field
potential.
