Perturbative Approaches to Modified Gravity

• Autores: Daniel Alejandro Molano Moreno
• Directores de la Tesis: Juan Gabriel Ramírez Rojas (dir. tes.), Pedro Bargueño de Retes (dir. tes.)
• Lectura: En la Universidad de los Andes (Colombia) ( Colombia ) en 2025
• Idioma: inglés
• Enlaces
  • Tesis en acceso abierto en: hdl.handle.net
• Resumen

  • Despite de success of General Relativity describing different phenomenology in different context, there are different kinds of motivation to think that general relativity needs an extension. In the last years the finding of these modifications of gravity has been a complex task with an abundance of proposals with field equations difficult where obtaining solutions for scenarios of physical interest is a highly intricate challenge. For that, we employ a rigorously established mathematical foundation rooted in perturbation theory in General Relativity (GR).

    First, we demonstrate that, for a significant class of vacuum f(R,RµνRµν) theories, the corresponding solutions do not yield additional effects beyond those predicted by General Relativity’s perturbation theory. However, models characterized by terms of the form f(R,RµνRµν,RµνσδRµνσδ) exhibit distinctive contributions not present in General Relativity. We assert that fundamental limitations exist, explaining why solutions of certain f(R,RµνRµν) models can deviate from their General Relativity counterparts, indicating non-connected solutions or non-analytic behavior. Conversely, in the models f(R,RµνRµν,RµνσδRµνσδ), the solutions seamlessly connect with those of General Relativity and we show and example in power Gauss-Bonet gravity and implications. This distinction highlights the nuanced interplay between higher-order curvature terms and their impact on gravitational dynamics, offering new insights into the landscape of modified gravity theories. Second, within the gauge-invariant framework devised by Nakamura, we have derived perturbation equations at both first and second orders for arbitrary backgrounds in f(R) theories of gravity. These equations are used in the context of cosmology, especially when dealing with first-order perturbations in f(R). Within this framework, we have successfully formulated gauge-invariant linear equations for scalar, vector, and tensor perturbations. This generalized formulation not only provides a comprehensive perspective on perturbations but also outlines a systematic approach for transitioning to specific gauges. Consequently, we have obtained and analyzed specific gauges, such as the Newtonian and synchronous gauges, within this formalism, and we have subsequently compared our findings with existing results in the literature.