Search for primordial symmetry breakings in CMB

There are possibilities to violate symmetries (e.g. parity and rotational invariance) in the primordial cosmological fluctuations. Such symmetry breakings can imprint very rich signatures in late-time phenomena, which may be possible to observe. Especially, Cosmic Microwave Background (CMB) will change its face drastically, corresponding to the symmetry-breaking types, since the harmonic-space representation is very sensitive to the statistical, spin and angular dependences of cosmological perturbations. Here, we discuss (1) general responses of CMB to the symmetry breakings, (2) some theoretical models creating interesting CMB signatures, and (3) aspects of the estimation from observational data.