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We explore the possibility of selecting a natural vacuum state for scalar andtensor gauge-invariant cosmological perturbations in the context of hybridquantum cosmology, by identifying those variables for the description of theperturbations that display a dynamical behavior adapted to the evolution of theentire cosmology. We make use of a canonical formulation of the whole of thecosmological system in which the perturbative gauge-invariant degrees offreedom are identified as canonical variables. Introducing background-dependentlinear canonical transformations on these perturbations and completing them forthe entire system, we are able to characterize a generic collection ofannihilation and creationlike variables that obey the dynamics dictated by arespective collection of Hamiltonians. We then impose that such Hamiltonianspossess no self-interaction terms so that, in a Fock representation with normalordering, they act diagonally on the basis of $n$-particle states. This leadsto a semilinear first-order partial differential equation with respect to thebackground for the coefficients that define the annihilation and creationlikevariables for all Fourier modes, as well as to a very precise ultravioletcharacterization of them. Such first-order equation contains, in the imaginarypart of its complex solutions, the complicated second-order field equation thattypically arises for the time-dependent frequency of the perturbations in thecontext of quantum field theory in curved spacetimes. We check that theasymptotic knowledge acquired allows one to select the standard vacua inMinkowski and de Sitter spacetimes. Finally, we discuss the relation of ourvacuum and the standard adiabatic vacua, and check that our asymptoticcharacterization of variables with a diagonal Hamiltonian displays theproperties that would be desirable for an adiabatic state of infinite order.

Hamiltonian diagonalization in hybrid quantum cosmology