The twistor lift of TGD forces the analog of Kähler form for M4. Covariantly constant sef-dual Kähler form J(CD) depends on causal diamond of M4 and defines rest frame and spin quantization axis. This implies a violation of CP, P, and T. By introducing a moduli space for the Kähler forms one avoids the loss of Poincare invariance. The natural question is whether J(CD) could relate to CP breaking for K and B type mesons, to matter antimatter asymmetry and the large scale parity breaking suggested by CMB data.
The simplest guess for the coupling strength of U(1) interaction associated with J(CD) predicts a correct order of magnitude for CP violation for K meson and for the antimatter asymmetry and inspires a more detailed discussion. A general mechanism for the generation of matter asymmetry is proposed, and a model for the formation of disk- and elliptic galaxies is considered. The matter antimatter asymmetry would be apparent in the sense that the CP asymmetry would force matter-antimatter separation: antimatter would reside as dark matter (in TGD sense) inside magnetic flux tubes and matter outside them. Also the angular momenta of dark matter and matter would compensate each other.
See the new chapter Breaking of CP, P, and T in cosmological scales in TGD Universe or the article with the same title.