Inflationary cosmology in RS-I

Abstract

In this work, I intend to show a possible candidate of inflaton potential V (φ) in a scenario of a brane world defined by a pair of branes (RS-I).The Inflationary Cosmology describes a phase in which our Universe evolves through accelerated expansion in a short time period at high energy scales. During this phase, our Universe is dominated by a potential V (φ) generated by a homogeneous scalar field φ(t) called inflaton. This potential must obey slow-roll conditions {ε, |η| 1} where ε and η are the slow-roll parameters. These parameters are given by [1]andWe can calculate the spectral index n(φ) and its derivate for this potential V (φ)andwhereThe amount of inflation that occurs is described by the number of e-foldings N, is given bywhere φ end is defined by ε(φ end ) = 1 if inflation ends through violation of the slow-roll conditions. The Brane Cosmology describes cosmological models with extra dimensions. A lot of interest in brane cosmology arose with a publication of two papers by Randall and Sundrum in the 90s. They propose a new higher-dimensional mechanism for solving the hierarchy problem building two models, RS-I [2] and RS-II [3]. In these two models, they consider that the Standard Model particles and forces, with exception of gravity are confined to a four-dimensional subspace, within the fivedimensional spacetime (bulk), referred to as 3-brane. Many researches have been done around this new cosmology as e.g. [9]. We choose the inflation in branes [4], [6], [7], [8].In this study, we consider that inflation might arise from the interaction potential between a 3-brane and anti-3-brane which are parallel and widely separated in five-dimensional Anti de Sitter space (AdS 5 ). The background is identical to that considered in the RS-I model [2].The potential between the branes is given by [4]The figures 1 and 2 show us the behaviours of the potential V (φ) and of the slow-roll parameters as a function of φ.The spectral index n and its derivate dn/dlnk can be related to N, respectively, asand 1 2Setting N = 70 (as usually done in inflationary scenarios) leads to n ≈ 0, 9714and dn dlnk ≈ −0, 0004, AcknowledgementThis work was supported by CNPq.