Strong gravity beyond general relativity

This thesis focuses on the application of numerical relativity methods to the solutions of problems in strong gravity. Our goal is the study of mergers of compact objects in the strong field regime where non-linear dynamics manifest and deviations from General Relativity could be found. We develop a new formulation of the Einstein equations in d+1 spacetime dimensions in the moving punctures approach, which leads to a well-posed set of equations for the Einstein-Gauss-Bonnet gravity (EGB), as well as for the most general parity-invariant scalar-tensor theory of gravity up to four derivatives (4∂ST). Using this formulation, we have implemented the equations of the 4∂ST theory in GRFolres, an open-source extension of our numerical relativity code GRChombo. This has enabled us to evolve equal and unequal-mass Binary Black Hole mergers in this effective field theory of gravity, as well as to study the loss of hyperbolicity and its relation to the weak coupling condition, among other topics of interest left for further study

Solving the initial conditions problem for modified gravity theories

Modified gravity theories such as Einstein scalar Gauss Bonnet contain higher-derivative terms in the spacetime curvature in their action, which results in modifications to the Hamiltonian and momentum constraints of the theory. In principle, such modifications may affect the principal part of the operator in the resulting elliptic equations, and so further complicate the already highly nonlinear, coupled constraints that apply to the initial data in numerical relativity simulations of curved spacetimes. However, since these are effective field theories, we expect the additional curvature terms to be small, which motivates treating them simply as an additional source in the constraints, and iterating to find a solution to the full problem. In this work we implement and test a modification to the CTT/CTTK methods of solving the constraints for the case of the most general four derivative, parity invariant scalar-tensor theory, and show that solutions can be found in both asymptotically flat/black hole and periodic/cosmological spacetimes, even up to couplings of order unity in the theory. Such methods will allow for numerical investigations of a much broader class of initial data than has previously been possible in these theories, and should be straightforward to extend to similar models in the Horndeski class

Qualitative study in Loop Quantum Cosmology

This work contains a detailed qualitative analysis, in General Relativity and in Loop Quantum Cosmology, of the dynamics in the associated phase space of a scalar field minimally coupled with gravity, whose potential mimics the dynamics of a perfect fluid with a linear Equation of State (EoS). Dealing with the orbits (solutions) of the system, we will see that there are analytic ones, which lead to the same dynamics as the perfect fluid, and our goal is to check their stability, depending on the value of the EoS parameter, i.e., to show whether the other orbits converge or diverge to these analytic solutions at early and late times.Comment: 12 pages, 7 figures. Version accepted for publication in CQ