Cosmology with Radion and Bulk Scalar Field in Two Branes Model

Abstract

We investigate cosmological evolutions of the bulk scalar field φ(t) and the radion d(t) in five-dimensional dilatonic two branes model. The bulk potential for the scalar field is taken as the exponential function V bulk ∝ exp(−2 √ 2bφ), where b is the parameter of the theory. This model includes Randall-Sundrum model (with b = 0) and fivedimensional Hořava-Witten theory (with b = 1). We consider matter on both branes and arbitrary potentials on the branes and in the bulk. These matter and potentials induce the cosmological expansion of the brane as well as the time evolution of the bulk scalar field and the radion. Starting with full five-dimensional equations, we derive four-dimensional effective equations which govern the low-energy dynamics of brane worlds. A correspondent five-dimensional geometry is also obtained. The effective fourdimensional theory on a positive tension brane is described by bi-scalar tensor theory.If the radion is stabilized, the effective theory becomes Brans-Dicke (BD) theory with BD parameter 1/2b 2 . On the other hand, if the scalar field is stabilized, the effective theory becomes scalar-tensor theory with BD parameter 3 2(3b 2 +1)where ϕ is the BD field defined by radion d(t). If we do not introduce the stabilization mechanism for these moduli fields, the acceptable late time cosmology can be realized only if the dilaton coupling b is small (b 2 < 1.6 × 10 −4 ) and the negative tension brane is sufficiently away from the positive tension brane. We also construct several models for inflationary brane worlds driven by potentials on the brane and in the bulk.

Regular collision of dilatonic inflating branes

“…The 4-dimensional effective theory valid at low energies for a system with 2 branes is derived in [15,16] and applied to a bulk scalar field in [17]. We will substitute the potentials from equations (1) and (2) into this low energy formalism to determine the validity of allowing free brane motion while constraining the bulk to the static metric given in [5].…”

“…In this section we will use the variables and parameters of [17], but to ensure we are describing the physical system set up previously, the parameters must be given by σ = σ 0 , V (φ) = −2δσ 2 e −2 √ 2bφ ,…”

Boundary inflation and the WMAP data

“…Besides the fields living on the positive tension brane (assumed to be our universe), the moduli associated with the position of the branes in the fifth dimension act as two non-minimally coupled scalar fields thereby leading to an effective biscalar-tensor theory of gravity [42,43,44,45,46,47,48,49]. Scalar-tensor theories have been intensively studied as natural extensions of General Relativity and are strongly constrained in the solar system [50,51].…”

“…A minimal realistic threefields model is considered: two of them being the moduli associated with the position of the branes in the extra dimension, and the other acts as a standard inflaton field living on our brane and coupled to the matter sector [43,44,45,46,68]. After a detailed analysis of the several viable background evolutions, we compute and discuss the primordial power spectra of the scalar and tensor perturbations generated during inflation.…”

Low energy effective action for Hořava-Witten cosmology

“…In the case of homogeneous cosmology, the field equations are derived and discussed in [8]. For a more thorough analysis, it would be nice if a purely 4-dimensional description of the braneworld exists.…”