Final answer:
Dark matter and dark energy are peculiar properties of our universe which the Big Bang theory does not fully explain. While redshift of galaxies and cosmic microwave background radiation are explained by the Big Bang theory, these two mysterious components, dark matter and dark energy, remain as significant unsolved puzzles in modern physics.
Step-by-step explanation:
The question asks which peculiar properties of our universe are not explained by the Big Bang theory. Among the listed options, A) Dark matter and dark energy are indeed peculiar aspects that are not comprehensively explained by the Big Bang theory. Dark matter is a form of matter that does not emit, absorb, or reflect light, identified through its gravitational effects. Dark energy is an even more mysterious form of energy that seems to be causing the accelerated expansion of the universe. While the Big Bang theory accounts for the creation of the universe and its initial expansion, it does not fully explain these strange components that make up a significant portion of the universe's total energy density.
The other options provided, including B) Redshift of galaxies, C) Cosmic microwave background radiation, and D) Expansion of the universe, are all phenomena that are successfully explained by the Big Bang theory. The redshift of galaxies provides evidence for the continuing expansion of the universe since the Big Bang, while the cosmic microwave background radiation is the afterglow of the initial explosion, cooled by the expansion to the current background temperature of the universe. Therefore, they are not peculiar properties unexplained by the Big Bang theory.