with the following correspondence: N = 2 n and R$_{c}$ = R$_{s}$ (2 nλ ) 1 / (2 n $^{+1)}$. (16) δ k ( t ) = δ$_{i}$ k ( t t$_{i}$ ) − $^{1}$±5 6 × $_{2}$F$_{1}$ ( ± 5 − √$_{33}$ 4(3 N + 4) , ± $_{5 +}$√$_{33}$ 4(3 N + 4) ; 1 ± 5 2(3 N + 4) ; − 3 ( N + 1) k 2 a 2 $_{i}$R 2 c ( t t$_{i}$ ) 2 N +8 / 3 ) (17) The two independent solutions of (13) in this regime read in terms of the hypergeometric function[15]. In the following discussion, we consider the upper sign solution only, because the other solution corresponds to the decaying mode and is singular at t → 0. Then the solution behaves as δ k ( t ) $^{t}$→ 0 − → δ$_{i}$ k ( t t$_{i}$ ) 2 3 and δ k ( t ) $^{t}$→∞ − −− → δ$_{i}$ k C ( k ) ( t t$_{i}$ ) − $_{1+}$√$_{33}$ 6 , (18) C ( k ) = Γ ( 1 + 5 2(3 N +4) ) Γ ( √$_{33}$ 2(3 N +4) ) Γ 1 + $_{5+}$√$_{33}$ 4(3 N +4) Γ $_{5+}$√$_{33}$ 4(3 N +4) [ 3( N + 1) k 2 a 2 $_{i}$R$_{c}$ ( 3 R$_{c}$t 2 i 4 ) N +2 ] − $_{5+}$√$_{33}$ 4(3 N +4) = Γ ( 1 + 5 4(3 n +2) ) Γ ( √$_{33}$ 4(3 n +2) ) Γ 1 + $_{5+}$√$_{33}$ 8(3 n +2) Γ $_{5+}$√$_{33}$ 8(3 n +2) [ 6 nλ (2 n + 1) k 2 a 2 $_{i}$R$_{s}$ ( 3 R$_{s}$t 2 i 4 ) 2( n +1) ] − $_{5+}$√$_{33}$ 8(3 n +2) , (19) t$_{i}$ = 2 3 √ 6 λR$_{s}$ sinh − 1 √ 1 − Ω$_{i}$ Ω$_{i}$ . (20) G$_{eff}$ = G ( 1 + 1 3 k $^{2}$/a$^{2}$m2 s 1 + k $^{2}$/a$^{2}$m2 s ) , (21) V ( r ) = − G r ( 1 + 1 3 e − m$_{s}$r ) , (22) respectively. The transfer function, C ( k ), is given by where Note that the effective gravitational constant (14) reads in the high-curvature regime when F ∼ = 1. In the position space, such a theory has the potential per unit mass [33] for such sufficiently small r for which time dependence of m$_{s}$ ( t ) may be neglected. Thus, each Fourier mode feels 4 / 3 times the conventional gravitational force if and only if k/a ( t ) ≳ m$_{s}$ ( t ) = (3 F ′ ) − 1 / $^{2}$. 8