Hierarquia e cosmologia em modelo de Randall-Sundrum

Abstract

Higher-dimensional theories have been considered since the early twentieth century by Nordstrom and then by Kaluza and Klein, and over the years, they have re-emerged in new contexts. In this work, we will discuss in a pedagogical manner the model presented in 1999 by Randall and Sundrum, which proposes an explanation to the so-called gauge hierarchy problem: the large discrepancy between the electroweak and the gravity scales of energy. As our language is general relativity, we devote the first chapter to developing its formalism, elucidating the topics necessary for understanding what will be addressed. Next, we introduce the Randall-Sundrum model. In this scenario, two branes are embedded in a (4+1)-dimensional Anti-Sitter spacetime, where one of them contains the fields of the standard model. We explore the gauge hierarchy for scalar, vector and spinorial fields. Finally, we discuss cosmology, where we review the (3+1)-dimensional conventional cosmology of the Friedmann-Robertson-Walker universes and then show how we can obtain an inflationary solution in the Randall-Sundrum model. We limit ourselves to the case where the distance between the branes is kept fixed.