The Hypersphere World—Universe Cosmology (WUC) addresses numerous unresolved issues in modern Astrophysics and Cosmology by providing alternative explanations to the prevailing Big Bang Theory (BBT). WUC solves critical problems such as: 1) The Hubble tension; 2) The missing baryon problem; 3) The origin of Fermi bubbles; 4) The age of the Universe discrepancy; 5) The coronal heating problem; 6) Internal heating and diversity of gravitationally-rounded objects in the solar system; 7) The presence of Plutonium-244, with an 80-million-year half-life, in nature; 8) Faster core rotations of the Sun and Earth compared to their surfaces; 9) The faint young Sun paradox; 10) The black-body spectrum of cosmic microwave background radiation.Additionally, WUC eliminates fundamental issues, including: 1) The need for the Universe to begin at t=0 , avoiding a temporal singularity; 2) The angular momentum problem in galaxies and extrasolar systems evolution; 3) The matter-antimatter asymmetry; 4) The magnetic monopole problem; 5) The uneven distribution of matter and voids; 6) Singularities leading to black holes; 7) The formation of supermassive black holes; 8) The "Axis of Evil" anomaly in cosmic microwave background measurements; 9) The wave—particle duality dilemma.