To describe the torsion in terms of the universe, I derived a form of the Friedmann equation, which itself was a form of a Lagrangian, \(\mathcal{L} = \frac{m\dot{R}^2}{2} - \frac{8 \pi GmR^2}{6} (\rho - k\sigma^2) + mc^2 \Lambda R^2\) If the cosmological constant is variable and corrected to the Planck length for a baby universe we have: \(\Lambda R^2 = \frac{R^2}{L_P}\) where σ plays the role of a spin density term \(\sigma = \frac{J}{V} = \frac{m \omega R^2}{L^3} = \frac{mvR}{L^3}\) in order for the negative value in - kσ² to cancel out the positive large value of mc²/6 ΛR² then the spin needs to match the observed dark energy density and the two have been given a relationship by Sivaram and Arun as: \(\frac{\Lambda c^2}{3} = \omega^2\) and \(\Lambda = \frac{3 \omega^2}{c^2} = 10^{-52}cm^{-2}\) which is the observed value of dark energy density. The torsion is \(Q = \frac{4 \pi G \sigma}{c^3} = 10^{-28} cm^{-1}\) and the background curvature of the universe is approximately the square of the torsion \(Q^2 \propto 10^{-56}cm^{-2}\) This is but, the most simplest kind of description of the torsion field of a universe. I cannot stress enough why having a universal rotation may be required in nature since spin and thus torsion would make it part of the full Poincare group of space symmetries, so it is something we might expect in nature. The fact it can answer for the expansion of a universe (and possibly inflation itself) is just a bonus. One argument some people may use is, ''if there was a universal rotation, why is there no evidence for it today?'' The answer is quite simple, not only has spin exponentially decayed since the primordial appearance of big bang, but there is actually even evidence for it today in the very slow but noticable phenomenon of dark flow, which is a mysterious directionality to the galaxies in the universe all in a common direction, which is itself a suspected phenomenon of dust inside a rotating Godel vacuum. Is itself, the energy associated to the vacuum as a coefficient to the cosmological constant. Notice, that if the cosmological constant term is related to the spin of a universe in such a way that it is identical to the dark energy phenomenon and that the spin of a universe is actually a variable (decaying since the beginning of big bang, as according to Hoyle and Narlikar as it should exponentially decay), \(\Lambda = \frac{3 \omega^2}{c^2} e^{-\lambda t}\) When I noticed this fact, I started to look into physical reasons why the rotation would effect the energy of a universe and I later found evidence from Fil'chenkov (which he has published in a number of different reputable journals) that a nucleating universe suffers energy loss from rotation: The rotation effectively lowers the Friedmann energy levels of a universe as it comes into birth (which also explains why the cosmological constant is so small - the negative torsion term is ''stealing'' energy from the nucleating vacuum). In saying this, why though would the torsion bring the energy of a universe down? In what manner say, does the torsion steal the energy? Well, it takes energy to make something spin, so that energy is being converted from the stored vacuum energy we associate to the cosmological constant into the spin energy for a universe. I expect if this is indeed true to what happened in this reality, then spin probably had a very important role which is better articulated than the expansion of a universe, it may have provided a certain stability to a nucleating universe as well ensuring it doesn't collapse back into the dense Planck phase too soon, but this [[may]] not be a problem as so far, high values corresponding to large cosmological vacuum densities in the primeval stages are notoriously a main factor of inflation theories, but it is one I can adopt in theory. There are two ways this can go and both of them do not originate in de Sitter space. The cosmological constant was either 1) Very high during the initial stages 2) Or very low but is increasing as the universes age progresses, with today's value corresponding to the observed value for vacuum energy. Option 1) gives us the most interesting physics because then the energy has dynamical uses - in terms of the spin and torsion. The solution is so natural and it really needs to catch on so that it can be studied further. It is a novel solution, providing explanations to: 1) The small observed value of the cosmological constant of order 10^-30g cm^-3 2) Dark energy in terms of an internal centrifugal force field term of the universe F(cent) = Ω²R(H), where R(H) is the Hubble radius. 3) Explains Dark Flow as the end phase of an exponential decay of the universal spin With possible new physics in: 1) Cosmological models that depart from the de Sitter vacuum (ie. varying energy density and so departing from the adiabatic system) 2) A varying cosmological term Just to note, any one of those universes I described, involves internal energy changes in the universe. The non-conserved Friedmann equation, with seven realistic effective density components looks like: \(\dot{R}\ddot{R} = \frac{8 \pi R^2}{6}[ \dot{\rho}_{on} + \dot{\rho}_{off} + \rho_g + \dot{\rho}_{EM} + \dot{\rho}_{vel} - \dot{\rho}_{\sigma} + \dot{\rho}_{vac}]\) The first and second density terms are the on-off shell components of matter fields in the universe, the third is the gravitational density, and in following order: the electromagnetic density, density due to velocities of particles, density due to spin (or torsion) and finally the density due to vacuum energy (which may or may not be the same thing as the of-shell matter term.
