Agullo I.Olmedo J.Sreenath V.2021-05-052021-05-052020Physical Review D Vol. 101 , 12 , p. -https://doi.org/10.1103/PhysRevD.101.123531https://idr.nitk.ac.in/handle/123456789/16293We derive a Hamiltonian formulation of the theory of gauge invariant, linear perturbations in anisotropic Bianchi I spacetimes, and describe how to quantize this system. The matter content is assumed to be a minimally coupled scalar field with potential V(φ). We show that a Bianchi I spacetime generically induces both anisotropies and quantum entanglement on cosmological perturbations, and provide the tools to compute the details of these features. We then apply this formalism to a scenario in which the inflationary era is preceded by an anisotropic Bianchi I phase, and discuss the potential imprints in observable quantities. The formalism developed here paves the road to a simultaneous canonical quantization of both the homogeneous degrees of freedom and the perturbations, a task that we develop in a companion paper. © 2020 American Physical Society.Article