Why Mature Galaxies Seem to Have Filled the Universe Shortly After the Big Bang — A New Cosmological Model, that Predicted the JWST Observations

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Introduction
This novel conceptual model upends the cosmological timeline, red-shifting, and accelerating universal expansion.This article begins by describing how global meridians, which are azimuthally projected onto a flat surface, are asymptotic along the surface, toward the horizon (away from the observer), in the familiar "Atlas" (gnomonic projected) mapping.By extension, the hypermeridians of a R 4 (four spatial) dimensional hypershere, azimuthally projected onto a R 3 (three spatial) dimensional sphere, are shown to be asymptotic along the spherical surface and also away from the observer.A coordinate system is presented (in a cross section) to equate red-shifting of wavelengths λ with azimuthal angular projections, Using this equation, red-shift (z) is revised from: z = .In conjunction with observed red-shifting survey data and Lambert's cosine law of luminous intensity, the universal hyperspere radius is estimated.From these established parameters, it is shown how both velocity and energy density appear to increase along azimuthally projected (skewed) length (x).As well, how galaxies appear to be dilated (or elongated), along the line of sight, with a resulting flattened rotation curve.From these established parameters, a function is developed to plot a curve, which is superimposed upon graphs (Distance modulus (µ) vs red-shift (z)) of data points from the HST Key Project.discrepancies between theoretical and observed galaxy rotation curves, as well as apparent increased energy density are shown to be predicted from this model.

Intuition of the Azimulthal Hyper-Projection Model of Cosmology
The familiar Atlas map, which is an R 2 azimuthal global projection, typically places Siberia and Alaska at opposite extremes.However, they are locally connected at the Bering Strait, as viewed in R 3 space.See figure 1. Hypothesis 1 (H1) As an Azimulthal Hyper-Projection onto spacetime is asymptotic to an outward horizon, the geometric perspective is based to the position of the observer, such that all projected geodesics will appear to be expanded outwardly, from the arbitrary biased perspective of the observer.This effect is similar to the familiar atlas map, which when viewed from North America, typically places Siberia and Alaska at opposite extremes.Therefore, the apparent distances between remote galaxies could actually be local neighbors, and vice versa, from their perspective.
Azimuthal Projections onto an R 2 Plane Appear to Expand Outward from the Observer, along the plane Figure 2 shows an observer on a R 2 plane, positioned along a tangent of a R 3 sphere, measures projected meridians at distance x n , per the equation [1]: Figure 3 shows how azimuthally projected meridians are asymptotic along the R 2 plane, and toward the horizon (away from the observer).
Figure 4 shows how azimuthal projections expansion is relative to the observer's position.On the left side, the observer is positioned along a tangent at projection a, and expansion increases toward point g .However on the right side, the observer is positioned along a tangent at projection g , and expansion increases toward point a.Figures 6 and 7 show how azimuthal projections red-shifting is relative to the observer's position.On the left side, the observer is positioned along a tangent at projection a, and red-shifting increases toward point g .However on the right side, the observer is positioned along a tangent at projection g , and red-shifting increases toward point a.A radical implication of this model is that azimuthal angular projections are positional dependent, thus degrees of redshifting over distance is positional dependent.It's conceivable that our local group would appear to be much more expanded, from the perspective of remote observer, and vice versa; vastly remote galaxies would appear to spaced much closer together, from the perspective of a remote observer.As Azimuthal projections are asymptotic along the observer's line of sight, obliqueness increases with distance x.Thus wave lengths become stretched along the observer's line of sight x.The observer in spacetime can not directly observe the projections in hyperspace, and is limited to his line of sight on the x direction.Figure 8 shows how the observer measures the wave lengths λ to be skewed (red-shifted).Section B − B , the "at rest" wavelength λ r est , is normal to the hypersheric surface.Oblique view A − A is the "observed" wavelength λ obs , with a skewed (elongated) wavelength.
5 Revised Formula for Red-shiff (z) Figure 9 is a 2 dimensional cross section of an R 4 (spatial dimensions) hypersphere Azimuthal projected onto a R 3 (spatial dimensions) sphere, and extended along X axis into macrospace.A classic space observer resides along the X axis at reference frame: x = 0, from which all measurements (x n ̸ = 0) are skewed projections, asymptotic to the horizon.Hyper-meridians and celestial bodies are Azimuthally projected as lateral straight lines, per equation 5: x n = R t an θ Solving for R: R = x n t an θ (4) Framed within this model, electromagnetic wavelengths of λ, along the hypersphere circumference of radius R, are considered to be at rest.However, x n is projected (skewed) along the X axis and observed with resulting redshift (z), similar to the redshifting equation [2]: In this alternative model,

Calculating the Universal Hypersphere Radius
The radius R of the hypershere can be deduced from a spacetime perspective (Where humans reside), by considering, that observed distance (x R ) must be equal to radius R when the tan of θ is equal to 1, or when θ = π 4 .Thus from the z value, where a = R π 4 , and Finding R from z = 0.273, using the approximate distance formula, In figure 9. Light-waves and energy density are constant along arc length a.However, Theorem 1 As R 5 hyper-spacetime is azimuthal projected onto R 4 spacetime, From the r.f. of an observer on the projected surface, topology is skewed (elongated), and appears expanded outward from the observer.As a result, celestial bodies appear to be traveling along expanded projected geodesics with increasing velocities (v).This apparent increase of velocity is equivalent to a decreased time interval (−∆t ).Light-waves appear to travel along X n with an increased velocity ⃗ v ′ of:

Calculating z per Distance x
Now that R (The radius of the hypersphere) has been established, values of z can be determined from any value of x n .Note that x n is a one dimensional cross-section of the space which humans measure galactic distance, although it is actually a skewed projection of hyper-arc length a onto classic space.Thus, from values of distance modulus µ and established radius R, theta is easily determined.Subsequently from theta, a is determined.Finally from equation 8, z is derived at any distance x n .

Energy Density Increases along Length X n
Corollary 1.1 As velocity along skewed x appears to increase per equation 18, energy density ρ proportionally increases, due to increased velocities in particle kinetic and internal energies (compression, energy of nuclear binding, etc.).The observer at x = 0 measures volume at x n [mpc] with increased energy density ρ n per equation:

Lambert's Cosine Law of Illumination
Consider that figure 9 describes an oblique projection of a source S with an illuminate value I .According to Lambert's Cosine Law of illumination [3], intrinsic values of such projected light will decrease in value with θ per equation: In this model, the luminous intensity of type Ia supernovae would decrease, accordingly.Thus, conventionally accepted standard candle measurements along x, would need to be recalculated per Lambert's Cosine Law.

Galaxy Rotation Curve with Increased Density
The discrepancies between theoretical and observed galaxy rotation curves involve both density and velocity.Conventionally, the dependence of circular velocity V ci r c on radial distance R assumes M , m and velocity to be fixed over large scales in Kepler's law, [4] Moreover, gravitational lensing demonstrates the existence of a much greater Mass (density) than the sum of the stars within the galaxy.However, this alternate model specifically addresses these two issues and provides an alternative explanation, Kepler's Law rearranged as density ρ integrated over time d t Corollary 1.2 Velocity ⃗ v and density ρ n are measured with increased magnitude per distance x n .This directly extends to energy density within galaxies and the effects on rotational velocity, such that: As x n increases, centripetal force is perfectly balanced by increases in ⃗ v and, subsequently, Note: total mass M inside the circle of the radius r can be obtained by doing integration of mass density in a volume.M = ρ n d t .ρ = ρ R and ρ M (Dark components are excluded from this model, with the intent of presenting an alternative).
Figure 11 shows how skewed projected meridians, along the observer's line of sight, appear elongated and are measured with greater density.The result is a flattened rotation curve, per x a .Thus, an elongated galaxy appears to have greater rotational velocity, and energy density.
Where K is a slope correction constant, which is necessary to offset conventional measurements of standard candle distances.
Table 1 lists extrapolated points, at 50(M pc) intervals, of Function .000, 5x10 8 .Also, corresponding values of µ and z Figure 12 shows the Function  13 shows the Function F : z → µ | F = µ, f (z) 0.000, 0.125 .Note the familiar curve (in logarithmic scale), which is conventionally interpreted as "accelerated expansion".9 Supportive Evidence of the R 5 Azimuthal Projection Model Galaxy Recession velocities (z red-shift and blue-shift) will be measured greater on the far side of galaxies.Such a closed system expanding in azimuthal projected hyperspace would defy the standard model of accelerated universal expansion and dark energy, where only space between galaxies are assumed to be expanding.Theorem 1, is supported by the following correlation study [5] "On Possible Systematic Redshifts Across the Disks of Galaxies" .This study shows a deviation from Kepler's orbital laws, specifically on the subject of increased velocity on the far sides of multiple galaxies.Although not conclusive, it does justify consideration to this article.Note that multiple galaxy surveys with increased velocities across their minor axis.Thus, velocity within the same body appears to increase per distance."Velocity observations in 25 galaxies have been examined for possible systematic redshifts across their disks: a possible origin for the redshifts could be the radiation fields.Velocities increase towards the far sides in most cases.This is so for the ionized gas, for neutral hydrogen, and in some cases for the stars.The effect is seen as velocity gradients along the minor axes, as well as in velocity fields of neutral hydrogen in other parts of the galaxies.Deviation of the kinematic major axis from the optical axis is found for 10 galaxies and in 9 of these the largest velocities occur in the far side.In the central regions of four galaxies are found large velocity gradients in the same direction.While expanding motions provide an explanation for some of these features, it remains difficult to thereby explain all the peculiarities found.Faintness of the data available in this preliminary study should be noticed.Observations specially programmed for this subject would be necessary."table 2 lists 25 galaxies, correlation coefficients and relevant columns (including sources of data): The Azimuthal Projection Model implies two observational phenomena for research and experimentation: • The planets in our solar system will deviate from their Kepler / Newtonian orbits by an increased radius and velocity, as their distance from Earth increases.Figure 14 is exaggerated for clarity.
• Two opposing zenith vantage points in the solar system (Earth vs the most outer region), in azimuthal projected hyperspace, will measure planetary distances as opposing skewed geometry, such that (respectively) projected distances are locally and remotely maximized.Figure 15 is exaggerated for clarity.The James Webb Space Telescope (JWST) observations of the most distant galaxies, some formed just 330 million years after the Big Bang when the universe was a mere 2 percent of its current age, appear as no less developed than our local group.Consequently, such observations compel theorists to rethink current standard models.Just as The Azimuthal Projection Model of Universal Expansion implies that our Milky Way galaxy's rotational curve would appear greatly accelerated and flattened from vast distances, it predicts the JWST observations as well.The fundamental concept of this model, is that redshifting is viewer dependent, and a function of projection at any given point.Thus, the radical implication is that the universe must be conceived of as a higher dimensional dynamic with spacetime as a limited projection which is viewer dependent, rather than as an arrow from absolute beginning of the big bang.

λ
obs −λ r est λ r est to be a function of distance x n and hyperspere arc length (radian) z = λ xn a −λ λ

Figure 1 :
Figure 1: Atlas map, which is an R 2 azimuthal global projection

Figure 2 :
Figure 2: R 3 sphere azimuthally projected onto a R 2 plane.Distance from angle θ and radius of sphere.

Figure 3 :Figure 5
Figure 3: meridians are asymptotic along the R 2 plane, and toward the horizon (away from the observer).

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Graphing a Function that conforms with the Hubble Diagram

Figure 12 :
Figure 12: Left: Function F : d → v, with extrapolated points.Right: Function F superimposed onto the HST Key Project

Figure 14 :Figure 15 :
Figure 14: Deviation from Theoretical Planetary Orbits Increases over Distance from Earth

Table 2 :
List of galaxies for which velocities along the minor axies are available.In successive columns: type; distance; angle between rotation axis of galaxy and line of sight; regression and correlation coefficients between velocity and distance; source of data