Post by: Dubbelosix on 08/08/2017 03:41:09
The time derivative of the Hubble radius is
Second derivative in time leads to acceleration (as would be expected say, in Friedmanns acceleration equation)
Third derivative in time leads to chaotic systems and is denoted as the jerk
The suggested equation for a non-conservation in particle number located in the effective density was suggested in a form (with rotation):
The rotating universe (at least in the early cosmology case) coupled to the dust inside of it strongly. This causes the charged particles in spacetime to experience a circular trajectory (in which they lose energy through the loss of radiation) which is known as a cyclotron radiation, similar to how we view charged particles accelerating in spacetime giving rise to Larmor radiation - in the case of gravity, this would be due to the weak equivalence principle.
here we use
notation for our third derivatives and higher since latex won't recognize dot notation**In which
. As noted by Arun and Sivaram, this leads to a path that is an exponentially increasing logarithmic spiral. Of course, in the context of a rotating expanding spacetime, the decaying rotational properties means that the logarithmic path too is overcome by expansion in the bigger picture. So instead of an exponential increase, the coupling of rotation to matter requires also that the coupling fall off as rotation equally decays. Such a logarithmic spiral would instead follow an exponential decay rule in accordance to the rotation which decays ~
We can see how this relates to the third derivative directly. Differentiation leads to in the spiral equation, terms that will fit the expanding and rotating Friedmann model
Notice, the potential difference, also known as the voltage
has picked up a charge to mass ratio coefficient,
We can replace the charge to mass ratio with a gyromagnetic ratio because the universes rotation, is also a classical property. This term that can replace the charge to mass ratio works only if charges in spacetime are distributed evenly. Due to spacetime homogeneity, this seems to be a fitting case. The interesting thing, the additional rotational radiation coming from these charged particles in the early universe can contribute to an exotic zoo. The high radiation densities would lead to new particles of various types. It also stands as a contributor to the background temperatures.
The differentiation of the spiral trajectory equation gives a solution which can fit previous terms investigated in the Friedmann power equation argued from a differentiation of a Friedmann Langrangian,
We may see how this differentiated version leads to comparable terms:
The rotating universe is compatible with the spiral paths taken giving rise to the extra radiation. Notice also, the differentiation of the spiral equation yields the jolt a rare symbol ever if there was one in physics
. Very rarely do we have to consider such derivatives but in this model, it cannot be avoided.ref: https://arxiv.org/ftp/arxiv/papers/1402/1402.5071.pdf
(note we have actually fixed an error in this work, whether it was a printing phenom or a copying related problem, the dimensions in the spiral trajectory equation have been fixed)
Post by: Dubbelosix on 08/08/2017 03:42:52
