Quantum aspects originated by Gravitation: from cosmology to astrophysics

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The study of quantum fields propagating in classical, curved and dynamical space-times offers a first approach to assess the consequences of the quantum theory when gravitational phenomena are not negligible. This is an important question that must be addressed when an intense gravitational field plays a principal role in the dynamics of a physical system, such as during the early universe (cosmological inflation) or in the formation of astrophysical black holes. One of the most striking features of this subject is perhaps that the calculation of physical observables, even for non-interacting fields, often involves ill-defined quadratic operators of fields. This feature introduces divergences in the observables, and thus requires dealing with non-trivial and suitable renormalization methods. The normal-ordering operation, usually employed in Minkowski spacetime, no longer works here, since additional ultraviolet divergences associated to curvature arise. The standard approach is to subtract the short-distance asymptotic behaviour of the appropriate two-point (Green) functions. As a consequence, unexpected results are predicted due to finite remaining terms, which are demanded by general covariance and appear closely related with the renormalization subtractions. The goal of this thesis is to give new insights following this direction. In the first part, we analyze the consequences of renormalization of quantum fields on diverse aspects of inflationary cosmology. Issues related to the ultraviolet divergences arising in the computation of the angular power spectrum of the CMB in the Sachs-Wolfe regime are first considered. Then we address the renormalization of the stress-energy tensor of matter (spin 1/2) fields during the early universe. We analyze this both when the matter fields are free and when they interact with the inflaton through Yukawa coupling. This is an important question in studies of inflation, preheating, or the subsequent expansion of the universe. Finally, the implications of "hidden" fields present during single-field inflation are also considered and physical consequences arising from CMB experimental bounds are discussed. In the second part of this thesis we analyze the impact of the quantization of fields on classical symmetries. The issue of renormalization here is of crucial importance since it can lead to the break-down of well-known classical symmetries and associated conserved Noether charges, yielding what is normally referred to in the literature as quantum anomalies. We will present a new and particularly interesting example of this feature in electrodynamics: the classical E-B duality symmetry of Maxwell equations without charges and currents fails to hold at the quantum level if spacetime has curvature and non-trivial dynamics. In fact, our results suggest that a dynamical curved spacetime with significant frame-dragging is able to distinguish between the two (left and right) circular polarization states of the photons. We shall also discuss some scenarios where this effect could take place. In particular, our analysis shows that a necessary condition is that the gravitational background admits the emission of gravitational waves. This offers promising physical implications in binary mergers in astrophysics, whose observational window is nowadays open thanks to the recent detections of gravitational waves by the LIGO-Virgo collaboration, as well as the advances in the studies of electromagnetic radiation in multi-messenger astronomy.
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