Cosmological Perturbations Induced by Ultralight Scalar Dark Matter: A Quantum Field Theoretic Perspective.

Abstract

The inhomogeneities in the early universe grow during the matter-dominated era, eventually giving rise to the large-scale structures we observe today. This growth is primarily driven by dark matter, which, at the onset of this epoch, is typically assumed to be either in a squeezed quantum state originating from inflation or in a mixed state resulting from possible thermalization with the primordial plasma. In this thesis, we develop a first-principles quantum-field framework to study the impact of an ultralight scalar dark matter field on linear cosmological perturbations during the matter-dominated era, working throughout with a generic Gaussian state that allows for a non-zero condensate, as well as quantum mixing and squeezing of modes. The problem is approached both with a fully quantum formalism and within a semi-classical framework. In the first part, we quantize both the matter field and the gravitational perturbation field. From this framework, we derive a set of coupled equations that describe the linear-order dynamics of the matter condensate and the two-point correlation functions. Through appropriate manipulations, we reduce the system to a closed equation for the graviton correlator. The self-energy appearing in such equation is shown to be formally identical to that obtained in the second, stochastic approach. In the second part, we treat the graviton perturbation as a classical stochastic field, while retaining a quantum description for the matter sector. We obtain a self-consistent equation of motion for the graviton one-point function. We compute and regularize the energy momentum tensor and self-energy for a generic Gaussian matter state within the adiabatic (WKB) approximation. The latter is shown to be valid for the range of masses of the scalar field m∼10−24 − 10−21 eV that we consider. Finally, we analyze the resulting equations for tensor perturbations in the transverse-traceless gauge and scalar perturbations in the longitudinal gauge, focusing on local backreaction effects of the quantum matter state. We argue how the oscillatory time dependence of the mass term of this equation could introduce in some limit a resonant solution.