GLYPH<BC>GLYPH<BA>GLYPH<BC>GLYPH<BH> GLYPH<BC>GLYPH<BA>GLYPH<BD> GLYPH<BC>GLYPH<BA>GLYPH<BD>GLYPH<BH> GLYPH<BC>GLYPH<BA>GLYPH<BE> GLYPH<BC>GLYPH<BA>GLYPH<BE>GLYPH<BH> GLYPH<BC>GLYPH<BA>GLYPH<BF> GLYPH<BC>GLYPH<BA>GLYPH<BD> GLYPH<BC>GLYPH<BA>GLYPH<BE> GLYPH<BC>GLYPH<BA>GLYPH<BF> GLYPH<BC>GLYPH<BA>GLYPH<BG> GLYPH<BC>GLYPH<BA>GLYPH<BH> GLYPH<BC>GLYPH<BA>GLYPH<BI> GLYPH<BC>GLYPH<BA>GLYPH<BJ> GLYPH<BC>GLYPH<BA>GLYPH<BK> GLYPH<BC>GLYPH<BA>GLYPH<BL> GLYPH<BD> χ ′ 1 [ M 5 / 2 ∗ ] φ ′ 1 [ M 5 / 2 ∗ ] µ 2 Σ$_{2}$ (4) R GLYPH<B9>GLYPH<BE> GLYPH<B9>GLYPH<BE> GLYPH<B9>GLYPH<BG> GLYPH<B9>GLYPH<BI> GLYPH<B9>GLYPH<BK> GLYPH<B9>GLYPH<BD>GLYPH<BC> GLYPH<BC>GLYPH<BA>GLYPH<BJ>GLYPH<BE> GLYPH<BC>GLYPH<BA>GLYPH<BI>GLYPH<BK> GLYPH<BC>GLYPH<BA>GLYPH<BI>GLYPH<BG> GLYPH<BC>GLYPH<BA>GLYPH<BI> GLYPH<BC>GLYPH<BA>GLYPH<BH>GLYPH<BI> GLYPH<BC>GLYPH<BA>GLYPH<BH>GLYPH<BE> GLYPH<BC>GLYPH<BA>GLYPH<BG>GLYPH<BK> GLYPH<BC>GLYPH<BA>GLYPH<BH> GLYPH<BC> GLYPH<B9>GLYPH<BC>GLYPH<BA>GLYPH<BH> FIG. 7: Level-curves of µ 2 and Σ$_{2}$ in the φ $^{′}$- χ ′ parameter space for example 2 with m 2 χ = − 0 . 5 M 2 $_{∗}$, µ 2 1 = − 0 . 25 M 2 $_{∗}$, Σ$_{1}$ = − 2 M 4 $_{∗}$, m 2 φ = 0 . 5 M 2 $_{∗}$, λ = 2 M − 1 ∗ , ξ = 6 M − 4 ∗ and Λ = 0. Circled are two points in the φ ′ $_{1}$- χ ′ 1 parameter space with the same values of µ 2 and Σ$_{2}$, corresponding to two solutions with the same Lagrangian. These solutions are plotted in Fig. 6. Working in the generalized longitudinal gauge (see appendix A for details), we introduce scalar perturbations Φ and Ψ and write the perturbed metric as and compute the linearized Einstein equations, yielding N + 1 dynamical equations for N + 1 scalar fields ( N fundamental scalars and one graviscalar, or radion). Since only N of these equations are independent, the Einstein constraint equations are used to eliminate ds 2 = a $^{2}$( y ) [ (1 + 2Φ( x, y )) γ$_{µν}$ ( x ) dx $^{µ}$dxν − (1 + 2Ψ( x, y )) dy $^{2}$] . (48) χ$_{a}$ ( x, y ) = ¯ χ$_{a}$ ( y ) + ξ$_{a}$ ( x, y ) , (49) Next we expand the N scalar fields to first-order in small perturbations ξ$_{a}$ ( x, y ) 21