Inflationary cosmology in RS-I

Abstract

In this work, I intend to show a possible candidate of inflaton potential V(phi) in a scenario of a brane world defined by a pair of branes (RS-I).

Inflationary cosmology in RS-I

Michele Ferraz Figueiró

Instituto de Física, Universidade de São Paulo Caixa Postal 66318, 05315-970, São Paulo-SP, Brazil

ABSTRACT

In this work, I intend to show a possible candidate of inflaton potential V(f) 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(f) generated by a homogeneous scalar field f(t) called inflaton. This potential must obey slow-roll conditions {e,|h| << 1} where e and h are the slow-roll parameters. These parameters are given by [1]

and

We can calculate the spectral index n(f) and its derivate for this potential V(f)

and

where

The amount of inflation that occurs is described by the number of e-foldings N, is given by

where f_end is defined by e(f_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 five-dimensional 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 (AdS₅). 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(f) and of the slow-roll parameters as a function of f.

The spectral index n and its derivate dn/dlnk can be related to N, respectively, as

and

Setting N = 70 (as usually done in inflationary scenarios) leads to

and

in excellent agreement with observational data from WMAP (0.94 < n < 1.00 and -0.02 < dn/dlnk < 0.02, [5])

Acknowledgement

This work was supported by CNPq.

Received on 17 October, 2005

• [1] A. R. Liddle, and D. H. Lyth, Cosmological Inflation and Large-Scale Structure , Cambridge University Press, Cambridge (2000).
• [2] L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999).
• [3] L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999).
• [4] G. Dvali and S.-H Henry Tye, Phys. Lett. B 450, 72 (1999).
• [5] H. V. Peiris, et al., Astrophys. J. Suppl. 148, 213 (2003).
• [6] S. Kachru, R. Kallosh, and J. Maldacena, JCAP 0310, 013 (2003).
• [7] C. Kolda, and D. H. Lyth, D-term Inflation and M-theory, [hep-ph/98122343].
• [8] B. Wang, C. Y. Lin, and E. Abdalla, Phys. Rev. D 69, 063507 (2004).
• [9] E. Abdalla, A. G. Casali, B. Cuadros-Melgar, Int. J. Theor. Phys. 43, 801 (2004).

Publication Dates

• Publication in this collection
  16 Jan 2006
• Date of issue
  Dec 2005

History

• Received
  17 Oct 2005