A Simpler Cosmology: Milne's Model
Cosmological General Relativity invokes Newton's Shell Theorem about a point of asymmetric contributions to Gravitational field in order to obtain an "observer dependent" gravitational field at every point in the universe. This paper shows the derivation of Newton's Shell Theorem and attempts to explain why, in an infinite distribution, a point of symmetry should be chosen where ρ/L²=ρ/R² is a function of R alone. The point of symmetry chosen must be the point where the gravitational field is actually being calculated. Furthermore, I present another calculation of the gravitational field using cartesian coordinates, but this method comes to g=(0,0,0), when a point of symmetry about the origin is selected.
The introduction of this text includes links to a number of demonstrations related to the Special Theory of Relativity created on "desmos calculator". There are also links to demonstrations of the cosmological distributions that are solutions to differential equations presented in Susskind's Cosmology Lecture 2. I have been posting this text as attachments in ResearchGate threads, but I decided to put it up as a "presentation" so that it can be found more easily.
This paper discusses why Milne's Model is not "empty" as many claim, but rather, has a negligible Gravitational Potential when compared to its Kinetic Energy content. There are two 1+1 spacetime diagram of the universe. The first imagines several phase transitions of the universe. In regards to the CMBR, the most important of these is the phase change from "Blackbody Spectrum" hydrogen to transparent hydrogen. An exaggerated diagram shows how the dipole anisotropy in the CMBR arises. Section 5 discuss how this model can account for the presence of redshift z=11 galaxies at 40 billion light-years away by using the concept of "peel-off-layers." Section 6 addresses potential concerns that peel-off-layers might be Lorentz variant.
https://en.wikipedia.org/wiki/Shape_of_the_universe discounts Milne's model, saying it is " It is incompatible with observations that definitely rule out such a large negative spatial curvature." What the article fails to acknowledge, though, is that the "negative spatial curvature" term in Friedmann Equations resolves to the equation "Distance = Velocity * Time". This statement is equivalent to the beginning of Newton's First Law: "An object in motion remains in motion at a constant speed". This law can only be made "large" or "small" in reference to phenomena that cause objects to accelerate (Gravitational Potential: Omega_M type phenomena), or cause distance to appear between objects due to some other effect other than velocity (deSitter; Omega_\Lambda type phenomena). However, recent observations of distant quasar groups have led to calculations of densities much greater than those predicted by the Lambda-CDM model. I posit that the most important feature, lacking in the Lambda-CDM model is acknowledgment that the primary cause of redshift is, in fact, neither gravitational, nor deSitter stretching of space, but the effect of an equipartition of radial rapidity, and the effect that equipartition has on densities of objects obeying "distance = velocity * time" which contemporary cosmologists inexplicably call "negative curvature"
Two exact solutions to the Friedmann equations are frequently mentioned. One is called a matter-dominated universe, where pressure = 0 which resolves to a(t) ∝ t ^2/3. I In the radiation dominated universe, p = 1 3 ρc^ 2 , and this resolves to a(t) ∝ t 1/2. I would like to introduce a third solution, which has the universe dominated by Kinetic Energy. In particular, what do we need to plug into the Friedmann equations for ρ, Λ and p to represent a universe where Kinetic Energy dominates, and the gravitational potential energy is relatively negligible?
I have been arguing for some time that cosmological inflation can be explained easily via Special Relativity. Just yesterday, it occurred to me how to estimate exactly what temperatures were needed to account for it. In this paper I imagine the end of the primordial universe, as the primordial gas reaches an age of 370,000 years, in a universe with a 25 billion light year radius. The time dilation factor is 68,000, and this can be achieved by a gas at a temperature of 1570 trillion Kelvin.