Some Aspects in Cosmological Perturbation Theory and ƒ (R) Gravity

General Relativity, the currently accepted theory of gravity, has not been thoroughly tested on very large scales. Therefore, alternative or extended models provide a viable alternative to Einstein’s theory. In this thesis I present the results of my research projects together with the Grupo de Gravitación y Cosmología at Universidad Nacional de Colombia; such projects were motivated by my time at Bonn University. In the first part, we address the topics related with the metric ƒ (R) gravity, including the study of the boundary term for the action in this theory. The Geodesic Deviation Equation (GDE) in metric ƒ (R) gravity is also studied. Finally, the results are applied to the Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime metric and some perspectives on use the of GDE as a cosmological tool are commented. The second part discusses a proposal of using second order cosmological perturbation theory to explore the evolution of cosmic magnetic fields. The main result is a dynamo-like cosmological equation for the evolution of the magnetic fields. The couplings between the perturbations in the metric and the magnetic fields are present in the dynamo equation, opening a new perspective in the amplification of magnetic fields at early stages of the universe expansion. The final part of this work is in the field of stellar kinematics in galaxies. It is a project that started at Sternwarte-Bonn Institut some years ago. Here we study the stellar and gas kinematics in HCG 90. Furthermore, we analyze the rotation curves and velocity dispersion profiles for the galaxies in the core of the group. Some possible future applications of the work are discuss

Primordial Magnetic Fields and the CMB

The origin of large-scale magnetic fields is one of the most puzzling topics in cosmology and astrophysics. It is assumed that the observed magnetic fields result from the amplification of an initial field produced in the early Universe. If these fields really were present before the recombination era, these could have some effects on big bang nucleosynthesis (BBN) and electroweak baryogenesis process, and it would leave imprints in the temperature and polarization anisotropies of the cosmic microwave background (CMB). In this chapter, we analyze the effects of a background primordial magnetic field (PMF) on the CMB anisotropies and how we can have sight the mechanisms of generation of these fields through these features. We start explaining briefly why primordial magnetic fields are interesting to cosmology, and we discuss some theoretical models that generate primordial magnetic fields. Finally, we will show the statistics used for describing those fields, and by using CLASS and Monte Python codes, we will observe the main features that these fields leave on the CMB anisotropies