Without relying on the cosmological principle, which has been the foundation of all the progress in physical cosmology such as the interpretation of Hubble’s law, Friedman-Roberson-Walker (FRW) metric in general theory of relativity, the expanding of the universe in the Big Bang theory, etc., but still disputable for its validity as a principle in physical science, we can find comprehensive explanations in 4-D complex space for many unsolved problems such as the variation of fine-structure constant on cosmological scale, dark matter (hypothetical matter) in astrophysics, dark energy (hypothetical energy) in physical cosmology, and so on. With introducing new galactic dynamo process, the cosmological magnetic fields, which has been one of unsolved problems in astrophysics, is explained. For physical cosmology in 4-D complex space, new theory is introduced.