Phenomenology of a massive quantum field in a cosmological quantum spacetime

We revisit the quantum theory of a massive, minimally coupled scalar field, propagating on the Planck-era isotropic cosmological quantum spacetime which transitions to a classical spacetime in later times. The quantum effects modify the isotropic spacetime such that effectively it exhibits anisotropies. Thus, the interplay between this quantum background and modes of the field, when disregarding the backreactions, gives rise to a theory of a quantum field on an anisotropic, dressed spacetime. Different solutions are found whose components depend on the quantum fluctuations of the background geometry. We construct a formal expression for the power spectrum of the scalar field fluctuations on such anisotropic background. It is shown that the anisotropy of this power spectrum is due to the modified frequency of the propagating quantum modes. This provides a quantitative estimate for the deviations from the isotropic power spectrum which can lead to the potential observational signatures on the cosmic microwave background. In addition, the problem of particle production when transitioning from such an effective spacetime to a classical one is reexamined. It is shown that particles are created, and the expectation value of their number operator depends on the quantum geometry fluctuations.

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