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Title: Quadratic scalar-tensor gravity
Author: Davies, Trevor Bamidelé
Awarding Body: University of Aberdeen
Current Institution: University of Aberdeen
Date of Award: 2017
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This thesis develops novel analytic models of scalar-tensor theories with quadratic coupling. In this framework, the coupling strength between scalar and matter is regulated in a way that allows the vacuum expectation value to vanish for low matter densities while becoming non-vanishingly large in the high-density regime. This results in significant deviations from the predictions of General Relativity in the strong-gravity regime. In astrophysics, we addressed the core-collapse supernova problem to account for the apparently missing energy required to explain the observed powerful explosions. We assumed a small, massless scalar gravitational field, thus allowing General Relativity to be recovered in the weak-gravity asymptotic limit. The non-trivial effects coming from the coupling function in the presence of a high-density field were analyzed at the instant of neutron star formation. Our results show that the scalar gravitational field evolves from a cosmological value to a new equilibrium via a Higgs-like mechanism. Additionally, the calculations associated with the gravitational binding energy shift and relevant relaxation timescale are explicitly shown. The full theory space of the model was also investigated for positive values of the coupling parameter. We studied a mechanism to address the stalled shock issue in core-collapse scenarios, which involved the application of sufficiently large positive values to the coupling parameter. Our results show that pulsating neutron stars act like optical cavities in which resonant scalar waves are parametrically amplified. It implies that the surface of a neutron star acts like an anti-phase reflector, releasing traveling scalar gravitational waves similar to an optical laser. In cosmology, the same framework was applied to a generic Friedman-Robertson-Walker universe involving general metric coupling and scalar potential functions. In cosmology, the same framework was applied to a generic Friedman-Robertson-Walker universe involving general metric coupling and scalar potential functions. We developed a mechanism which allowed the scalar field to be dynamically trapped, thus generating a potential capable of driving primordial inflation. Our results show that a trapped scalar field produces non-trivial dynamical consequences when applied to standard cosmology. Additionally, our analytic solutions for the generic inflationary behaviour, produce acceptable duration and e-foldings, thus recovering the Hubble parameter which is consistent with the present-day value. A feature of our cosmological model is that the universe can undergo several accelerating or decelerating phases, even though the scalar potential and metric coupling are monotonic functions overall. As this is important for the current dark energy problem, the quasi-static motion of the gravitational field induced by the scalar potential in the early universe, is investigated for a small value of the scalar field with normalized metric at the present time. Our results show that a variable Lambda Cold Dark Matter universe emerges naturally from the quadratic model.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Gravity ; Mathematical physics ; Tensor fields ; Scalar field theory ; Dark matter (Astronomy)