0 2 4 6 8 10 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 l$_{1}$ C GLYPH<LParen1> L,l, l 1 , l 2 GLYPH<RParen1> (a) Case 1: Plot of C ( L, ℓ, ℓ 1 , ℓ 2 ) for ˜ Δ LM 10 ( k, τ s ); with initial multipoles ℓ 3 = 1 , ℓ 4 = 0, the final multipoles being ℓ = ℓ 2 = ℓ 1 + 1 (blue, solid) and ℓ = ℓ 2 = ℓ 1 − 1 (red, dashed) respectively. The terms are non-zero only when the index of deviation from statistical isotropy L = | ℓ 3 − ℓ 4 | = 1. 0 2 4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 l$_{1}$ C GLYPH<LParen1> L,l, l 1 , l 2 GLYPH<RParen1> (b) Case 2: Plot of C ( L, ℓ, ℓ 1 , ℓ 2 ) for ˜ Δ LM 20 ( k, τ s ); with initial multipoles ℓ 3 = 2 , ℓ 4 = 0, the final multipoles being ℓ = ℓ 2 = ℓ 1 (blue, solid) and ℓ = ℓ 2 = ℓ 1 − 2 (red, dashed) respectively. The terms are non-zero only when the index of deviation from statistical isotropy L = | ℓ 3 − ℓ 4 | = 2. 0 2 4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 1.2 l$_{1}$ C GLYPH<LParen1> L,l, l 1 , l 2 GLYPH<RParen1> (a) Case 1: Plot of C ( L, ℓ, ℓ 1 , ℓ 2 ) for ˜ Δ LM 11 ( k, τ s ); with initial SH multipoles ℓ 3 = ℓ 4 = 1, the final SH multipoles being ℓ = ℓ 1 − 1(= ℓ 2 − 1) and the index of deviation from statistical isotropy L = 0 (blue, solid), L = 1 (red, dashed) and L = 2 (black, dot-dashed) respectively. 0 2 4 6 8 10 GLYPH<Minus> 2.5 GLYPH<Minus> 2.0 GLYPH<Minus> 1.5 GLYPH<Minus> 1.0 GLYPH<Minus> 0.5 0.0 0.5 l$_{1}$ C GLYPH<LParen1> L,l, l 1 , l 2 GLYPH<RParen1> (b) Case 2: Plot of C ( L, ℓ, ℓ 1 , ℓ 2 ) for ˜ Δ LM 22 ( k, τ s ); with initial multipoles ℓ 3 = ℓ 4 = 2, the final multipoles being ℓ = ℓ 1 (= ℓ 2 ) and the index of deviation from statistical isotropy L = 0 (blue, solid), L = 1 (red, dashed) and L = 2 (black, dot-dashed) respectively. FIG. 2: Evolution of the coefficient of the spherical Bessel functions, C ( L, ℓ, ℓ 1 , ℓ 2 ) with multipole moment ℓ 1 as in equa- tion (31), for non-zero off-diagonal terms of a unit normalized ˜ Δ LM ℓ 3 ℓ $_{4}$( k, τ s ) FIG. 1: Evolution of the coefficient of the spherical Bessel functions, C ( L, ℓ, ℓ 1 , ℓ 2 ) with multipole moment ℓ 1 as in equa- tion (31), for non-zero diagonal terms of a unit normalized ˜ Δ LM ℓ 3 ℓ $_{4}$( k, τ s ) namely ˜ Δ LM 11 ( k, τ$_{s}$ ) and ˜ Δ LM 22 ( k, τ$_{s}$ ) with L = 0 , 1 , 2, for possible values of ℓ and ℓ$_{2}$ . Figure 2 shows the evolution of the coefficients for off- diagonal, unit normalized ˜ Δ LM 10 ( k, τ$_{s}$ ) and ˜ Δ LM 20 ( k, τ$_{s}$ ), for possible values of L, ℓ and ℓ$_{2}$ . The coefficients for off- diagonal ˜ Δ LM ℓ$_{3}$$_{,ℓ$_{4}$}$( k, τ$_{s}$ ) vanish for L = 0 i.e. the statistical isotropic case. Setting L = 0 , M = 0 we recover the statistical isotropic case as in equation (10), section (II D). The transfer of power of the statistical anisotropic terms to higher SH multipoles ℓ$_{1}$ & ℓ$_{2}$ due to free streaming is illustrated in figures (1) and (2). Starting from a unit normalized ˜ Δ LM ℓ$_{3}$$_{,ℓ$_{4}$}$( k, τ$_{s}$ ), we plot the evolution of the coef- ficients in equation (32), C ( L, ℓ, ℓ$_{1}$, ℓ$_{2}$ ) with ℓ$_{1}$ for specific values of the SH multipole moments ℓ$_{3}$ and ℓ$_{4}$ . We find that the values of ℓ and ℓ$_{2}$ are constrained by the values of ℓ$_{1}$ due to the triangular inequalities of the Clebsch- Gordon coefficients. Figure 1 shows the evolution of these coefficients for diagonal, unit normalized CMB brightness fluctuations The ability to measure violation of statistical isotropy at low SH multipoles is largely compromised by cosmic variance. At larger SH multipoles, the effect due to viola- B. SI violation at large multipoles 6