This novel hypothesis uses mathematics in the form of topology. The goal: to establish a “proof of concept” to which equations can be added, by anyone. It’s concluded the Steady State, Big Bang, Inflation and Multiverse theories all ultimately fail and a topological model including bits (binary digits), Mobius strips, figure-8 Klein bottles and Wick rotation works better. The failed cosmologies have impressive good points leading to the idea that they’re all necessary stepping-stones. For example, the Big Bang is seen here as violation of the 1st Law of Thermodynamics but its supposed origin from quantum fluctuations is reminiscent of bits switching between 1 and 0. The topological hypothesis has potential to explain dark matter (DM), dark energy (DE) and electromagnetic-gravitational union. This model predicts (1) the universe’s nature is binary and topological, (2) antigravitons are the quanta of dark energy, (3) dark energy has no connection with the expanding universe since there never was, nor will be, expansion or contraction (dark energy comprises dark matter – in some dimensions, dark matter’s being composed of dark energy will follow DE=DMc^2: in others, it won’t), (4) immortality, and (5) imprints in the Cosmic Microwave Background from gravitational waves will oneday be detected unambiguously and not interpreted as evidence of inflation. The article “post-dicts” Special Relativity’s time dilation as well as existence of both curvature and flatness in space-time. Finally, the article introduces what is called vector-tensor-scalar geometry - and extensions of Einstein's Gravity and Maxwell's Electromagnetism.