Boson stars, baby universes and wormholes in a modified gravity scenario
The absence of a well-established theory concerning gravity and its behavior at high energies demands a global effort to construct a viable quantum theory for the gravitational field. The complexity of this issue calls for a multidisciplinary approach, that incorporates a wide range of viewpoints, from sophisticated mathematical tools and statistical techniques to ambitious experiments. A deep understanding of our fundamental theories, their capabilities and limitations, as well as an improvement of the main roads in them are essential steps towards achieving the ultimate goal, the development of a satisfactory theory that combines gravity and quantum physics. This PhD thesis is situated within this context, with particular emphasis on investigating the existence and properties of exotic compact objects resembling black holes. In the last decade, we have witnessed significant technological advancements that have transformed the direct observation of extremely compact astrophysical objects into a reality. This has highlighted that the black holes predicted by Einstein's General Theory of Relativity are consistent with observations. However, given that the current precision of gravitational wave observatories and very long baseline radio astronomy observatories, such as the LIGO-Virgo-KAGRA collaboration and the Event Horizon Telescope, is not sufficient to unequivocally confirm the Kerr hypothesis, which stands that all black holes in the Universe are described by the Kerr metric, it becomes necessary to consider alternative explanations that allow us to confront the data with potential deviations from General Relativity. These deviations are expected both for theoretical considerations linked to quantum gravity and for phenomenological reasons related to the potential existence of sources of dark matter and energy. These sources are crucial to justify the standard cosmological model and the growth of large-scale structures. Exploring alternatives beyond General Relativity is challenging, primarily due to technical complexities, as equations become highly intricate and, analytical and numerical methods are not developed or optimized beyond General Relativity. Obtaining analytical solutions that accurately depict compact objects is, in itself, a formidable challenge. Moreover, the endeavor to extract gravitational wave profiles for studying the merger processes of these compact objects, in order to extract characteristic information from these theories, presents an even greater challenge. Recently, alternative gravity theories that are likely to have an optimal analytical and numerical treatment have been characterized. By formulating gravity theories in metric-affine-type manifolds where the gravitational Lagrangian is an arbitrary function of traces of the Ricci tensor and the metric, it is possible to establish a correspondence between the solution space of General Relativity and these theories. This facilitates discovering solutions and studying their dynamical properties within these alternative theories by solving similar problems within the framework of General Relativity. Furthermore, among the wide range of exotic compact objects detailed in the literature that could potentially exhibit characteristics similar to black holes, boson stars occupy a prominent role. Unlike conventional stars, predominantly composed of fermionic matter, boson stars are formed by bosonic particles and described by scalar or vector fields. Consequently, when referring to boson stars we do not refer to a unique singular entity but instead to an entire family of astronomical objects which depend on the specific boson that constitutes them. It can be found in the literature that boson stars have a significant potential to mimic part of the phenomenology of black holes, as they share multiple similarities in various observational aspects. Due to all these effects and with the aim of maintaining simplicity in the resulting equations at an acceptable level, we will dedicate our study to the conjunction between boson stars and alternatives to the General Theory of Relativity. Derived from the outcomes of this study and driven by curiosity and the will to explore the boundaries of established gravitational scenarios, we will also delve into the concept of wormholes, a topological phenomenon widely popularized by science fiction. This concept allows for the identification of two spatially separated regions connected by a sort of spacetime tunnel. The foundational principles underlying these objects and the observable consequences they entail can offer valuable insights in our quest to deepen our understanding of the constraints governing gravitational models.