This speculation is the logical continuation of the previous one [viXra:2006.0202]. It describes a cosmological model with a 4d hypersphere, in expansion, on the surface of which our Universe extends, but as will see, with an internal part that has its own role. The involvement of the fourth spatial dimension is unavoidable but it does not imply reintroducing the concept of an absolute space and not even that of absolute time. On the contrary, the model excludes both. The geometry described finds an application in the calculations of Galactic Recession: those calculations are confirmed here after adding gravity. In this subsequent formulation an explanation is sought as to why, in this "empty" space, a ray of light is bound to move on the 4d hypersphere surface. Then, we proceed by building a physical model, in which that empty space is filled with matter and radiation, and we try to check for any flaws. We will also show that this geometry, with its expansion mechanism, infers General Relativity. Given the constant expansion speed hypothesized for the Universe, no redshift is due to expansion itself. Here the Cosmological redshift is Gravitational or Doppler. In this conjecture the surface of the 4-sphere (like a kind of bubble expanding over time) goes through a continuum of states of equilibrium in which an internal pressure exerted by a radiation, in a reversible adiabatic expansion resulting from the Big Bang, balances the cohesion of the Universe whose surface tension is due solely to the pressure of the Cosmic Background Radiation. Resulting model is an approximation for the Galaxy Epoch and it is based on the Einstein’s solution for weak fields to the field equation of General Relativity. You can use this only in the context of observable Universe, during the lasts 10 billion years. These following points can have interesting consequences: 1.this geometry infers General Relativity which, in this way, is not considered a consequence of postulates 2.there is an energy exchange between the surface and its interior so that the two sides could communicate The implication is that what is on the surface is constrained by the speed of light c but, admitting the existence of the tachyon, what can enter the 4d hypersphere is not, being bound to a different space-time interval. This last idea could be developed by linking to phenomena that violate the relativistic laws as Quantum Non-Locality. About the pros and cons on the model: 1.Advantages: Galactic Recession and Relativity separation, Inferred and non-postulated Relativity. Possibility of admitting the tachyon if the underlying idea is developed. 2.Disadvantages: Need the internal part but not dark matter and dark energy. Weakness regarding the Covariance Principle but the effect is limited to large interstellar distances. Finally, it is important to point out that this speculation leads to a falsifiable theory.