The Hubble Field vs Dark Energy, Part II: The Lagrange-Hamilton Equation and Some Concepts on Force, Energy and Tensors in the Hubble Field

Abstract

In a recent article [1] the author of this Part II proposed the parameter Γ H for the acceleration expansion of the Universe, instead of dark energy, defining such parameter as Γ H =H 2 ⋅ r (M/S 2 ) = a constant. A question about the expansive and constant acceleration of the internal levels of the Universe could be solved by equation ((3.10) ref. [1]) of the same article: Any assumed internal distance, lower than r of (ref. [2]) implies a proportional change in the squared Hubble parameter, so maintaining the constancy of the Γ H value for every stratum of the Universe. In the present work it is proved the constancy of the Hubble force by means of its generalized coordinates. As well, an equation to relate the Lagrange and the Hamilton functions is obtained for the Hubble field. Two concepts for both Hubble’s energy and tensor are also proposed. Finally, prior misprints of Part I, ref. [1], are corrected in the Appendix.