9 SH multipoles where the significance is largely obscured by dominance of cosmic variance. However, SI violation at small SH multipoles in the baryon-photon plasma at last scattering would free-stream to large SH multipoles at present, and consequently, would be easier to establish from CMB observations. A program of study to relate the BipoSH brightness fluctuations in the baryon-photon fluid for different physical scenarios is currently under- way. We have used our formalism to represent and match the well known case for SI violation in presence of a ho- mogeneous magnetic field. We illustrate how the angular correlations in such a case could be seeded by the dipole term of the generalized CMB brightness fluctuation and would have diagonal ( ℓ ′ = ℓ ) and off-diagonal ( ℓ ′ = ℓ ± 2) terms. coefficients to SI deviations in the baryon-photon fluid, as well as, the primordial power spectrum. The observable BipoSH coefficients can be compactly expressed in terms BipoSH brightness fluctuations terms through products of standard Clebsch-Gordon coefficients and a Wigner-9j function. We also present the expression for the simpler case of an isotropic primordial power spectrum, where the BipoSH coefficients turn out to be given through a com- pact combination of a Wigner-6j symbol and a Clebsch- Gordon coefficient. We also provide the large SH mul- tipole limit for these coefficients for the terms encoding deviations from SI at low BipoSH multipoles. We obtain the generalized free-stream evolution equa- tion for the SI violation encoded in terms of the Bi- poSH brightness fluctuations introduced in our work. We demonstrate that different modes BipoSH brightness fluctuations at the present epoch have to evolve from same Bipolar modes at the last scattering. The moments of the CMB brightness fluctuations ˜ Δ LM ℓ$_{1}$$_{ℓ$_{2}$}$( ˆ k, τ$_{s}$ ) at last scattering are expected to non-zero at small values of SH multipoles ℓ$_{1}$ and ℓ$_{2}$ due to tight coupling. However, our results show that the power in these SI violating terms at low SH multipoles would be transferred dur- ing free-stream evolution to higher multipoles ℓ$_{3}$ and ℓ$_{4}$ in ˜ Δ LM ℓ$_{3}$$_{ℓ$_{4}$}$( ˆ k, τ ) at the present epoch. This is akin to the well known free-streaming evolution of power in the SI brightness fluctuation at low SH multipole power at last scattering to large SH multipole at present. For clearly highlighting the structural similarity, we present the evo- lution of BipoSH brightness fluctuations in the asymp- totic case of large values of the final SH multipoles today relative to the initial SH multipoles at last scattering. While many of the claimed observational evidence of SI breakdown, such as the “axis of evil”, “north-south asymmetry” etc., pertain to relatively small values of the In summary, our work strongly motivates closer study of all possible SI violating phenomena and scenarios in the simple baryon-photon plasma, since these could po- tentially provide more readily observable signature of SI violation in the universe. It is also encouraging that it may have observational implications in light of the recent WMAP-7 discovery [4]. Since, the quadrupolar anisotropy anomaly with non-zero BipoSH coefficients re- lated as A 2 M ℓℓ ∼ − 2 A 2 M ℓ − 2 $_{ℓ}$, rule out an origin in anisotropic power spectrum, this may well be related to SI violations in the CMB brightness fluctuations. This possibility is also bolstered by the fact that the non-SI effect peaks at acoustic l ∼ 200 scales pointing to some non-trivial physics at the last scattering surface. Extension of this formalism to CMB polarization should be readily possi- ble. The formalism and the initial conclusions are impor- tant and timely in light of higher precision and resolution CMB anisotropy and polarization data expected in near future, in particular, from the ongoing Planck Surveyor CMB mission. The BipoSH coefficients are defined in equation (19). For a directional dependent primordial power spectrum as in equation (16), these Bipolar coefficients can be evaluated using the angular correlations in equation (17) in the following way We use the following symmetry properties of the Clebsch-Gordan coefficients in equation (8.4.10) from [48] Appendix A: Bipolar coefficients for SI deviations A JN ℓℓ ′ = ( A JN ℓℓ ′ ) l =0 + $^{√$_{4}$$_{π}$}$∫ k $^{2}$dk 2 π 2 P$_{0}$ ( k ) ∑ l ℓ$_{1}$ℓ$_{2}$LL ′ Π$_{ℓ}$$_{1}$$_{ℓ}$$_{3}$ Π$_{ℓ}$$_{2}$ β$_{ℓ}$$_{1}$$_{ℓ}$β ∗ ℓ$_{2}$ℓ ′ C ℓ$_{2}$ 0 ℓ$_{1}$ 0 l 0 ∑ m g lm ∑ MM ′ ˜ Δ LM ℓ$_{1}$ℓ ( k, τ ) [ ˜ Δ L $^{′}$M ′ ℓ$_{2}$ℓ ′ ( k, τ )] ∗ × ∑ m$_{1}$m$_{2}$mm ′ ( − 1) m $^{′}$C LM ℓ$_{1}$m$_{1}$ℓm C L $^{′}$M ′ ℓ$_{2}$m$_{2}$ℓ ′ m ′ C JN ℓmℓ ′ − m ′ C ℓ$_{2}$m$_{2}$ ℓ$_{1}$m$_{1}$ $_{lm}$. (A1) C ℓ$_{2}$m$_{2}$ ℓ$_{1}$m$_{1}$ ln = ( − 1) l + ℓ$_{1}$ − $^{ℓ$_{2}$}$C ℓ$_{2}$ − m$_{2}$ ℓ$_{1}$ − m$_{1}$ l − m = ( − 1) ℓ$_{1}$ − $_{ℓ$_{2}$}$Π$_{ℓ}$$_{2}$ Π$_{ℓ}$$_{1}$ ( − 1) $^{m}$C ℓ$_{1}$m$_{1}$ ℓ$_{2}$m$_{2}$ l − m (A2)