Hubble’s relation and It’s exponential generalization with Cosmological Applications

Hubble’s law reveals how the components of the universe adhere to overarching dynamical rules on a cosmological scale. While it is most renowned for describing the universe's expansion, a general displacement equation derived in alignment with this law, along with a general equation of converging displacement, has been applied to estimate the time remaining before the Milky Way and Andromeda collide. This estimate closely aligns with results from numerical simulations of other studies. Additionally, the implications of this generalized equation provide valuable insights into key cosmological enigmas, including the time variation of the Hubble parameter, the cosmological past incompleteness, and the enduring mystery of the relationship between the subtle value of the cosmological constant and the quantum zero-point energy of the vacuum. It has also been successful in explaining the structure of spiral galaxies.