Gravitation and cosmology: structural questions and applications

Abstract

In the last decade new observational and theoretical results have given a new impulse on the investigation of structural questions and phenomenological applications of general relativity. On one hand, cosmology is in a period where new data suggest new and challenging visions of the universe. In this context, new approaches are necessary to explain what is observed and also what is not directly observed. On the other hand, a hole new set of theoretical possibilities were open with the so-called anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. This correspondence suggests a deep relation between gravity and problems relating field theories and integrable models. This project proposes to investigate structural questions and possible applications in these great lines of research. Concerning cosmology, we focus on aspects related to the characteristics of dark matter and energy, especially in cases where it is possible to formulate dark energy settings distinct from the standard model, where the cosmological acceleration is generated by a cosmological constant. In the latter case, the dynamics being described by a standard field, there must be an interaction between the matter and energy sectors, possibilities which we have being treating and constraining in terms of observations. From the observational point of view, we are proposing to be members of the J-PAS project, that will get, among other results, an excellent catalogue of galaxies and quasars permitting a precise measurement of the matter power spectrum and the baryonic acoustic oscillations, leading to a measurement of the dark energy equation of state parameter with a precision better than 4%.Going from cosmological to astrophysical scales, we propose to investigate systems with cylindrical and axial symmetries in d-dimensional models. Of particular interest are black hole solutions. Such scenarios include black holes and ring holes in brane world models and in the Gauss-Bonnet gravity. The focus will be non-asymptotically flat solutions. Basic aspects to be treated are thermo dynamical and dynamical stability of the systems to be considered. Perturbing the known solutions of the gravity theories considered, both the Einstein gravity as well as its variations, we not only study their basic structures but also their implications with the use of the AdS/CFT relation, involving condensed matter theories of physical interests in the CFT side. In this case, models describing superconductors and superfluids have being emphasized in the pertinent literature and will be research topics in this project. The AdS/CFT correspondence gives us a link between gravity and field theories. Integrable models have well defined relations with gauge theories within this celebrated relation, being considered themselves a topic of study. In this context, we will treat a series of problems associated with the formulation of the quantum inverse scattering method applied to twisted and Temperley-Lieb algebras. (AU)