Belfiglio, Alessio (2024) Quantum entanglement in cosmological scenarios: momentum and position-space techniques. [Tesi di dottorato]

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Abstract

We investigate quantum entanglement in cosmological scenarios, focusing on entanglement generation in primordial particle creation processes and entropy characterization in black hole settings. We first show how entanglement entropy can be quantified in expanding backgrounds from particle production mechanisms, adopting momentum-space techniques and generalizing previous investigations in Friedmann-Robertson-Walker and anisotropic spacetimes to the presence of small inhomogeneities. In particular, we analyze some promising single-field inflationary scenarios, in agreement with current observational data, where the presence of spacetime perturbations can be traced back to the fluctuations of a scalar inflaton field. We compute the $S$ matrix associated with such fluctuations, showing that inhomogeneous particle production is typically non-negligible in large-field scenarios. We focus on pair production, observing that the presence of inhomogeneities allows for mode-mixing in such creation processes, which is not conversely found in homogeneous scenarios. The corresponding particle density leads to a nonzero momentum-space entanglement entropy, quantified via the von Neumann entropy of the reduced state obtained by tracing out one of the two halves of the bipartition. We also observe that the Hubble horizon emerges as the natural separation scale for field modes during inflation, arguing that entanglement dynamics across such horizon may be crucial in order to address the quantum-to-classical transition of primordial fluctuations and to clarify the role of vacuum energy throughout the universe evolution. In the second part of the work, we turn to black hole scenarios and we explore the possibility of interpreting Bekenstein-Hawking entropy in terms of quantum entanglement. In particular, we study the ground state entanglement entropy of a discretized scalar field in static, spherically symmetric backgrounds, focusing on the widely-studied entanglement area law for singular and regular black hole solutions. Working in position space, we first discretize the field Hamiltonian by introducing a lattice of spherical shells and imposing a cutoff in the radial direction. Then, we obtain the ground state of the field, also considering possible couplings to the spacetime scalar curvature. Accordingly, we compute the corresponding von Neumann entropy by tracing out the degrees of freedom residing inside a given sphere, which plays the role of the horizon. We select the Schwarzschild-de Sitter, Hayward and Bardeen spacetimes, also discussing some recently proposed quantum black hole metrics. We show that the presence of field-curvature coupling can alter the entropy scaling with respect to the boundary area, thus violating the area law for sufficiently large coupling constants. We also observe that entanglement characterization close to a black hole horizon captures relevant information about its thermodynamics, suggesting that horizon thermodynamics may in itself be of quantum origin. Additional insights on the entanglement thermodynamics of black holes are then obtained by investigating their core properties. In particular, we highlight that entanglement energy may allow to discriminate between singular and regular black hole solutions, showing possible departures from area law in the Reissner-Nordstr\"om background geometry. Our outcomes then indicate that the interpretation of black hole thermodynamics in terms of entanglement, despite promising, necessarily requires a more refined description of black hole degrees of freedom and their corresponding dynamics, especially at Planck scales.

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