An Alternative to Dark Matter? Part 3: An Open Universe (3 Gy to 76 Gy) Galaxies and Structures Rotation

A cosmological model was developed using the equation of state of photon gas, as well as cosmic time. The primary objective of this model is to see if determining the observed rotation speed of galactic matter is possible, without using dark matter (halo) as a parameter. To do so, a numerical application of the evolution of variables in accordance with cosmic time and a new state equation was developed to determine precise, realistic values for a number of cosmological parameters, such as energy of the universe U, cosmological constant EΛ, curvature of space k, energy density ρΛe, age of the universe tΩ (part 1). That energy of the universe, when taken into consideration during the formation of the first galaxies (<1 [Gy]), provides a relatively adequate explanation of the non-Keplerian rotation of galactic masses (part 2). Indeed, such residual, non-baryonic energy, when considered in Newton’s gravity equation, adds the term FΛ(r), which can partially explain, without recourse to dark matter, the rotations of some galaxies, such as M33, UGC12591, UGC2885, NGC3198, NGC253, DDO161, UDG44, the MW and the Coma cluster. Today, in the MW, that cosmological gravity force is in the order of 1026 times smaller than the conventional gravity force. The model predicts an acceleration of the mass in the universe (q~-0.986);the energy associated with curvature Ek is the driving force behind the expansion of the universe, rather than the energy associated with the cosmological constant EΛ. An equation to determine expansion is obtained using the energy form of the Friedmann equation relative to Planck power PP and cosmic time or Planck force FP acting at the frontier of the universe moving at c. This constant Planck force, from unknown sources, acts everywhere to the expansion of the universe as a stretching effect on the volume. Finally, the model partly explains the value a0 of the MOND theory. Indeed, a0 is not a true constant, but depends on the cosmological constant at the time the great structures were formed (~1 [Gy]), as well as an adjustment of the typical mass and dimension of those great structures, such as galaxies. The constant a0 is a different expression of the cosmological gravity force FΛ as expressed by the cosmological constant, Λ, acting through the energy-mass equivalent during the formation of the structures. It does not put in question the value of G.