It is well established that the evolution of the universe is described by the standard hot big bang model. Its early stage oers a common eld for particle physics and astrophysics. Various observations in laboratories have given some clues to understand what occurred in the early universe. Moreover, new ideas have also led to resolutions of the problems concerning the very early universe. For example, grand unied theories (GUTs) with strong rst-order phase transitions led to the idea of in ation, and dark matter may be explained by new physics, which will be examined in the near future. On the other hand, astrophysical observations give constraints on models of particle physics, which cannot be obtained from accelerator experiments.
In this thesis, we would like to concentrate on three topics: (1) the cosmological birefringence; (2) the baryon asymmetry of the Universe (BAU); and (3) the large-scale
hypermagnetic fields.

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