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 fend is defined by e(fend) = 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
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Publication in this collection
16 Jan 2006 -
Date of issue
Dec 2005
History
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Received
17 Oct 2005