This paper introduces the Hypergeometrical Universe (HU) Theory, a groundbreaking cosmological model that proposes a new shape and structure for the universe: the Lightspeed Expanding Hyperspherical Universe (LEHU). In HU, the universe began through a "Big Pop" event—a metric fluctuation driven by the Heisenberg Principle, rather than a singularity. This fluctuation initiated distinct cosmic phases—Blackholium, Neutronium, and Neutrinium—each associated with specific densities, states of matter, and degrees of freedom that drove cosmic evolution. Central to HU is the concept of matter emerging from deformed space, simplifying physics by reducing the universe to interactions between space, deformed space, and time. This model replaces complex mass and field-based theories, allowing natural laws to be derived from first principles. During phase transitions, such as the Blackholium-Neutronium shift, the universe acquired an extra degree of freedom with neutron formation, leading to observable oscillations in the Cosmic Microwave Background (CMB). The later Neutronium-to-Baryonic phase generated Baryonic Acoustic Oscillations (BAO), further imprinted in the CMB and reflective of the HU model’s unique particle interactions. To validate this framework, HU achieved the hyperspherical harmonic spectral decomposition of the CMB, addressing the complexity of observations by precisely locating Earth's position in the hyperspherical universe. Hyperspherical harmonics are not a complete basis set for data collected on a spherical surface, such as the CMB; therefore, HU’s accurate spectral decomposition required pinpointing Earth’s coordinates within this topology. By leveraging this spectral information, HU constructs a comprehensive 3D map of the universe, capturing cosmic structures with unprecedented clarity and validating HU’s predictions. This model has far-reaching implications for understanding cosmic origins, matter formation, and the inherent structure of space. HU presents a vision of the universe that challenges conventional models, offering new explanations for phenomena like the homogeneity of the CMB, the absence of antimatter, and the bounded nature of kinetic energy. This paper invites theoretical and experimental physicists to explore HU’s powerful framework, with computational models and spectral maps available to further investigate this transformative view of cosmology.