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My earliest attempt at properly justifying the zero origin universe within the microwave background data failed because I failed to recognize many flaws in my reasoning at the time. Attempt no.2 was fairly well demolished in a rather lengthy debate over the way in which I had combined blackbody curves, and how those curves came to be. I was thus forced to go back to square one and do it all over again. It seems I may have it right this time.
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The CMBR monopole spectrum graph is supposedly the expanded blackbody temperature plot of the early universe after it had evolved for 300,000 years, expanded over a distance of as much as 10 million light years (the goal posts keep changing), at which time it had cooled to 4000 degrees K, being the temperature threshold where hydrogen was no longer ionized. The universe became fairly abruptly transparent and all of the previously entrapped radiation was released into the universe from everywhere to travel the universe to everywhere.

A background radiation is also expected in a zero origin universe, but certainly not for the same reasons. The temperature of that universe would range from absolute zero at the origin to its current temperature. And because the universe has evolved from nothing, there can be no doubt that it will continue to evolve. The rate of that evolution is clearly demonstrated in the red shifting of the characteristic spectral lines of the elements per increasing distance into the past. A mandatory consequence of the increasing redshift per distance in a non expanding universe is that the universe was colder in the past, not hotter.

The very early universe would have remained relatively unchanged for a very long time (relative to the current time rate) and the temperature of the entire universe could be summed up as a general heat source (but not a blackbody) and averaged to give a temperature that represents the heat of the universe at the time, and whatever curve shape the combined temperatures generate, the power curve will peak at a specific wavelength. That wavelength can represent the entire spectrum for that era in the evolution of the universe. The relationship between the curve peak and the rest of the spectrum at the time would remain consistent as the universe evolves. i.e. If the temperature of the peak is doubled, the wavelength at the peak will be halved. And the same conditions will apply to every other wavelength of the spectrum.

The purpose of the next image is only to graphically demonstrate that all wavelengths halve if the temperature is doubled. Each curve in the graph was computer generated using Planck's blackbody equation for emissive power per wavelength. The power spectrums have been brought into an alignment using multipliers so that they can be directly compared.

Notice that the curve shape is always exactly proportional no matter what temperature it's plotted for? Those proportions never change. The power peak of any blackbody spectrum can be adjusted with a multiplier so that it peaks at the same level as a curve who's shape is to be tested against a blackbody spectrum, and then a multiplier sets the peak of the spectrums to align at the same wavelength, and it always tells the same story. The fit with the blackbody curve will never vary, no matter what radiator temperature is used in the test. Or, the test curve itself can be varied with a simple multiplier so that it can be compared with a specific curve, and exactly the same story unfolds. The test spectrum also never changes.

The set of black curves in this image are extensions of the 8 K curve, created with simple multipliers. Each wavelength in the 8 K spectrum is multiplied by, *1, *2, *4 and *8. Notice that the curves are identical to those in the previous image.

The green curve is the spectral energy density spectrum for a 2 K temperature curve, just for a shape comparison with the (black) emissive power per wavelength curves. At no time will the relationship between the emissive power per wavelength spectrum and spectral energy density spectrum alter.

Since the evolution of the universe is dependent on interactions between existing matter, the more advanced the stage of evolution the faster will be its development. The universe is necessarily heating up at an exponential increasing rate, so the time allocated to any given temperature must be reducing inversely to that rate.

Neither the origin nor the present will contribute to the background. Background radiation curves can then be plotted within the parameters of, infinite background emissions of zero energy (1 x 0), and zero background emission in the present (0 x 1).

The black curve in the next graph was generated according to those conditions. The yellow curve was generated likewise, but the whole x-scale is shifted so that the zero mark aligns with the .34mm wavelength mark. The reason for this is that the entire spectrum of the obviously visible universe is not represented in the CMBR. The 13E+9 light year chunk of the past since the big bang universe became transparent can't be included as a component of the background radiation in that universe, and since the zero origin curve is compelled to obey big bang's rules, the present for that curve is necessarily set in the past by 13E+9 years, when the zero origin universe was in a lesser evolved state. However, the curve shape will never change, no matter what stage of evolution it's plotted to. The .34mm x-scale offset was chosen because it was the best fit, I certainly couldn't predict it. But this time it should help to determine how far and how fast the universe is evolving.

The curve shape will remain constant regardless of where the cutoff point is set, but the power peak will of course vary as the cutoff point is varied, increasing dramatically as the cutoff point nears the present. I would think that should have been obvious.

The power peak of the 13 billion year offset graph is naturally set to what is observed.

There is now one major difference in that the power attributed to a representative wavelength for a stage of evolution is raised to the fifth power instead of the fourth, as previously. The zero origin curve is now not a particularly good fit with the 2.73 blackbody curve in the longer wavelength zone, but it doesn't need to be. It had always concerned me that the power peak of a blackbody spectrum for a specific temperature increases 32 times when the temperature is doubled, while I was allowing for only a 16 fold increase.

Exactly the same wavelength-power relationship will prevail regardless of what kind of spectrum a wavelength belongs in, so long as the conditions that create the spectrum shape don't change. Double the temperature and the power received from any equivalent wavelength (halved wavelength) in the newly generated spectrum will have increased 32 fold. And it doesn't have to be an enclosure in thermal equilibrium either. The only significance of that, is that it produces a specific spectrum shape.

The following is extracted from the program that plotted the curves for the zero origin universe. It will make a lot more sense as it is than if I try developing any sort of formula from it.

    a = a + .005 
' "a" are stages of evolution in steps 
' from 0 to 1 in increments of .005

    IF a > 1 THEN END

    b = 1 - a ^ 2       
' "b" stores the power ratio per time rate
' of evolution at each step of "a".

    wl = (1 / a) - 1  
' The initial time zone wavelength on the graph plot is 199mm. 
' That's the first step recorded from infinity, and the universe 
' had then already existed for an eternity. That wavelength 
' bridges the infinite time gap to the zero origin, and blends 
' in with the next evolution stage. There are of course no 
' discrete stages.

    zl = (b * a) ^ 5 * 28000
' "b * a" sets the power for the stage of evolution. That result 
' is now raised to the fifth power because that's the rate at which 
' each wavelength of a power spectrum increases per temperature 
' increase. That rule applies for every object in the universe. 
' Double its temperature and the emissive power at each halved 
' (equivalent) wavelength increases 32 fold. 

' "28000" is a multiplier for curve comparison. Such a multiplier 
' sets the power peak, and does not change the curve shape one bit. 
'-------------------

This is the complete Qbasic program. 
Copy it directly off this screen and paste it into Notepad, then 
save it as .BAS file. 

'---Program start------------------------------------

' Control and Break breaks out of any Qbasic program.

' Anything preceded by the  '  is to be read as is.
' It's not part of the program.

'----------------------------------------------------
    
    CLS
    SCREEN 12

    COLOR 8
    LINE (10, 150)-(500, 150)     'Grid lines
    LINE (10, 200)-(500, 200)
    LINE (10, 250)-(500, 250)
    LINE (10, 300)-(500, 300)
    LINE (10, 350)-(500, 350)
    LINE (10, 400)-(500, 400)
    LINE (100, 120)-(100, 410)
    LINE (150, 120)-(150, 410)
    LINE (200, 120)-(200, 410)
    LINE (250, 120)-(250, 410)
    LINE (300, 120)-(300, 410)
    LINE (350, 120)-(350, 410)
    LINE (400, 120)-(400, 410)
    LINE (450, 120)-(450, 410)
    COLOR 15: LINE (500, 120)-(500, 410)
   
    pi = 3.14159
    c = 3E+08
    k = 1.3807E-23
    h = 6.6262E-34
   
    ON TIMER(1) GOSUB tfix ' The next eight lines set the program
    TIMER ON               ' run speed to suit your computer.
    WHILE stp < 10
    pp = pp + 1
    WEND
tfix:
    ti = (pp / 10)
    TIMER OFF
   
cm$ = "8 mm.  7     6     5     4     3      2     1     0 "
    COLOR 7
    LOCATE 27, 13: PRINT cm$
    COLOR 12: LINE (485, 400)-(485, 450)
    COLOR 11: LOCATE 11, 24: PRINT "2.73 K blackbody spectrum"
    LOCATE 12, 22: PRINT "(emissive power per wavelength)"
    t = 2.73
   
aa: q = q + 1: w = q / 20
    f = c / (w * .001)

   ' Emissive power per wavelength.
x = (2 * pi * h * c ^ 2) / (w ^ 5 * ((EXP((h * f) / (k * t))) - 1))
    z = x * 1.22E+20
          ' 1.22E+20 is a power multiplier for curve comparison.

'----------------Zero origin universe-------------

    a = a + .005
' "a" are stages of evolution in steps
' from 0 to 1 in increments of .005

    IF a > 1 THEN GOTO ab

    b = 1 - a ^ 2
' "b" stores the power ratio per time rate
' of evolution at each step of "a".

    wl = (1 / a) - 1
' The initial time zone wavelength on the graph plot is 199mm.
' That's the first step recorded from infinity, and the universe
' had then already existed for an eternity. That wavelength
' bridges the infinite gap to zero, and blends in with the next
' evolution stage. There are of course no discrete stages.
    
    zl = (b * a) ^ 5 * 28000
' "b * a" sets the power for the stage of evolution. That result
' is now raised to the fifth power because that's the rate at which
' each wavelength of a power spectrum increases per temperature
' increase. That rule applies for every object in the universe.
' Double its temperature and the emissive power at each wavelength
' increases 32 fold.

' "28000" is obviously a multiplier for curve comparison. Such
' a multiplier sets the power peak, and will not change the curve
' shape one bit.
'------------------------------------------------
   
    CIRCLE (500 - (w * 50), 400 - z), 1, 11
' 2.73 blackbody plot per Planck (emissive power per wavelength).
   
    CIRCLE (483 - (wl * 50), 400 - zl), 1, 12
    CIRCLE (500 - (wl * 50), 400 - zl), 1, 15
' The time-distance covered by the final step to the present on the
' zero origin curve is designated a wavelength of .34mm, hence the
' 483 instead of 500 in the circle statement.

  '  IF w > 10 THEN GOTO ab
    FOR tt = 1 TO ti: NEXT tt
    GOTO aa

ab: COLOR 15: LOCATE 14, 18: PRINT "Zero origin spectrum at t-0 years."
    COLOR 12: LOCATE 16, 18: PRINT "Zero origin spectrum at t-13"
    LOCATE 17, 18: PRINT "billion years relative to now."
    LOCATE 28, 11
    PRINT cm$
    COLOR 7: LOCATE 1, 1
PRINT "The curve shape will remain constant regardless of where"
PRINT "the cutoff point is set. The power peak will of course"
PRINT "vary as the cutoff point is varied, increasing dramatically"
PRINT "as the cutoff point nears the present. I would think that"
PRINT "should have been obvious."
PRINT
PRINT "The power peak of the 13 billion year offset graph is naturally"
PRINT "set to what is observed."

'---Program end------------

Something that has bothered me for some time is the fact that even at the peak of the hype for an expanded blackbody explanation for the CMBR, the raw monopole spectrum data was conspicuously absent, while the dipole data was clearly set out for all to see. Since I've never come across any raw data for the monopole, I've had to improvise by using the raw dipole spectrum data.

Because the dipole is taking the same picture of the cosmic background as the monopole, by default it has the same spectrum as the monopole. Apart from its power peak falling a long way short of the all sky spectrum, the only difference is that the entire spectrum has been slightly red or blue shifted depending on which way the dipole is being measured. What I can't understand though is why the following dipole graph, which was plotted with the raw dipole data set, shows such an enormous blue shift. The peak of its spectrum has been shifted to that of a 3.4 K radiator. That represents a substantial velocity relative to the cosmic background. Whatever the reason though, it must generate the same curve as the all sky picture.

In trying to compare curves in the graph, I found it easier to shift the monopole curve to align with the dipole than vice versa. The monopole is shifted to the right with a multiplier based from the zero mark on the graph scale. And that adjustment is quite valid for the purpose of the comparison. As you can see, the monopole was certainly no exact match with the raw dipole data, and as a consequence would be no better a match with the raw monopole data, if it could be found.

I've also included the trailing end of a 13 degree K plot, which only indicates the presence of the galaxy. The galaxy power spectrum is not in proportion of course, but the curve mismatch on the hotter side of the graph could be adjusted all over the place by making different assumptions regarding dust and thermal contributions to the data from the galaxy.

The CMBR graph for the zero origin universe was plotted along a line between the origin and the present and is therefore plotted on intensity per wavelength. It can of course also be plotted according to spectral energy density. Or I can simply convert the intensity per wavelength to spectral energy density. The conversion is very simple. c/(w*pi^.5) does the x-scale conversion. Then the power attributed to each wavelength on the intensity per wavelength scale is raised to power^.5 which converts the emissive power curve to the realm of spectral energy density. The entire power spectrum of the blackbody enclosure can be elevated to the scale of the spectral energy density realm and the curve shape can, with an appropriate power multiplier, be directly compared with anything else plotted in that realm, but not outside that realm.

For the sole purpose of comparing curve shapes, there is nothing whatever wrong with converting between emissive power per wavelength and energy density per frequency, nothing at all. Swapping between frequency and wavelength doesn't alter anything because the two properties of the single entity are inseparable. And I can choose any graph scale I like for the energy density per frequency, even if the x-scale happens to coincidentally align with a linear wavelength scale.

The curves in the two frames of this animation were plotted accordingly. They compare the monopole curve and the zero origin curve (which has been elevated to the realm of spectral energy density with appropriate multipliers), with the graph plotted from the raw dipole data, which has been shifted to the colder end with a multiplier so that it can be directly compared when the power spectrums of each are set to peak at the same height. Once again, that method of comparison is quite valid. Notice how close a fit the zero origin curve is?

(animation)

Using an x-scale where frequency is linear hides a substantial curve misalignment between the raw dipole data and the 2.73 K spectral energy density plot (monopole) on the lower frequency end of the graph.