Perturbaciones cosmológicas en teorías de gravedad escalar-tensor

Motivados por el creciente auge de estudios en teorías de Gravedad Modificada (TGM), se estudian las teorías de Brans-Dicke, Escalar-Tensor y f(R), las cuales son un grupo de estas modificaciones de la Relatividad General. En el presente trabajo, se hallan, las ecuaciones de campo, las ecuaciones Friedmann para un universo homogéneo e isotrópico y las perturbaciones cosmológicas para cada una de las teorías anteriormente expuestas. Además de hallar las perturbaciones cosmológicas en forma general, se calculan éstas para un universo de dominio de materia, encontrando así las ecuaciones tipo Poisson para las teorías de gravedad Escalar-Tensor y f(R). Luego, se muestran las equivalencias entre las teorías de gravedad EscalarTensor y f(R), en todos los desarrollos que se hicieron a lo largo de la tesis. Por último, se muestra como calcular los potenciales partiendo de dos ejemplos específicos de f(R), los cuales son, el modelo de Starobinsky y el modelo de Hu-Sawicki, encontrando así, todas las equivalencias entre las teorías.Abstract: Motivated by the growing rise of studies in theories of Modified Gravity (TGM), the theories of Brans-Dicke, Scalar-Tensor and f(R) are studied, which are a group of these modifications of General Relativity. In the present work, we find, the field equations, the Friedmann equations for a homogeneous and isotropic universe and the cosmological perturbations for each of the theories previously exposed. In addition to finding the cosmological perturbations in a general way, these are calculated for a domain of matter domain, thus finding the Poisson equations for the Scalar-Tensor and f(R) gravity theories. Then, the equivalences between the ScalarTensor and f(R) gravity theories are shown in all the developments that were made throughout the thesis. Finally, we show how to calculate the potentials from two specific examples of f(R), which are, the Starobinsky model and the Hu-Sawicki model, finding all the equivalences between the theories.Maestrí

Accelerating Universe and the Scalar-Tensor Theory

To understand the accelerating universe discovered observationally in 1998, we develop the scalar-tensor theory of gravitation originally due to Jordan, extended only minimally. The unique role of the conformal transformation and frames is discussed particularly from a physical point of view. We show the theory to provide us with a simple and natural way of understanding the core of the measurements, Λobs ∼ t0−2 for the observed values of the cosmological constant and today’s age of the universe both expressed in the Planckian units. According to this scenario of a decaying cosmological constant, Λobs is this small only because we are old, not because we fine-tune the parameters. It also follows that the scalar field is simply the pseudo Nambu–Goldstone boson of broken global scale invariance, based on the way astronomers and astrophysicists measure the expansion of the universe in reference to the microscopic length units. A rather phenomenological trapping mechanism is assumed for the scalar field around the epoch of mini-inflation as observed, still maintaining the unmistakable behavior of the scenario stated above. Experimental searches for the scalar field, as light as ∼ 10−9 eV, as part of the dark energy, are also discussed