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We use the method of the Lewis-Riesenfeld invariant to analyze the dynamicalproperties of the Mukhanov-Sasaki Hamiltonian and, following this approach,investigate whether we can obtain possible candidates for initial states in thecontext of inflation considering a quasi-de Sitter spacetime. Our main interestlies in the question to which extent these already well-established methods atthe classical and quantum level for finitely many degrees of freedom can begeneralized to field theory. As our results show, a straightforwardgeneralization does in general not lead to a unitary operator on Fock spacethat implements the corresponding time-dependent canonical transformationassociated with the Lewis-Riesenfeld invariant. The action of this operator canbe rewritten as a time-dependent Bogoliubov transformation and we show that itsgeneralization to Fock space has to be chosen appropriately in order that theShale-Stinespring condition is not violated, where we also compare our resultsto already existing ones in the literature. Furthermore, our analysis relatesthe Ermakov differential equation that plays the role of an auxiliary equation,whose solution is necessary to construct the Lewis-Riesenfeld invariant, aswell as the corresponding time-dependent canonical transformation to thedefining differential equation for adiabatic vacua. Therefore, a given solutionof the Ermakov equation directly yields a full solution to the differentialequation for adiabatic vacua involving no truncation at some adiabatic order.As a consequence, we can interpret our result obtained here as a kind ofnon-squeezed Bunch-Davies mode, where the term non-squeezed refers to apossible residual squeezing that can be involved in the unitary operator forcertain choices of the Bogoliubov map.

Dynamical Properties of the Mukhanov-Sasaki Hamiltonian in the context of adiabatic vacua and the Lewis-Riesenfeld invariant