I am the LORD that maketh all things;
that stretcheth forth the heavens alone;
that spreadeth abroad the earth by Myself;
That frustrateth the tokens of the liars,
and maketh diviners mad;
that turneth wise men backward,
and maketh their knowledge foolish;
Isaiah 44:24,25
Astronomers have published their analyses of the redshifts, angular sizes, and/or brightnesses of galaxies from JWST deep fields.
Most of the redshifts were estimated by photometry and are reported in the publications with 1σ random error generally less than 0.5. The uncertainty of size estimates is typically around 15%. In cases where the researchers published only their estimated linear radius of galaxies in kiloparsecs, we converted this back to angular diameter using the cosmological parameters assumed in that study, thereby recovering their original observed angular sizes. For completeness, we also included HST data on lower-redshifted galaxies by Trujillo et al. (2004).
The curve reflecting the correct cosmology should bisect these
values. We can already see that the ΛCDM curve does not remotely match the data at high redshifts. To see which curve best fits the data, it is useful to bin the data into groups by redshift (z), taking the median value of z and angular size (θ) for each bin in these magnitude-limited surveys. Using the median reduces the influence of galaxies whose redshift or size has been incorrectly estimated. The median values for each bin are indicated by the square, and the standard deviation is shown by the vertical lines.
Clearly the data are remarkably consistent with the Doppler model; all the median values are within one standard deviation, and several are nearly centered on the predicted curve itself. None of the data are within one standard deviation of the ΛCDM curve. Given the scatter in the data and the uncertainty of the median size of a typical galaxy in magnitude-limited surveys, the tired light model cannot be eliminated on the basis of these observations.
These angular diameter observations are particularly useful because of the drastic difference between the predicted sizes based on ΛCDM expansion versus Doppler motion. And these differences grow wider with increasing redshift. At a redshift of 15, the angular size prediction of the Doppler model is 6.6 times smaller than that of the ΛCDM model. At a redshift of 20, the ratio goes up to 8.3.
The curve reflecting the correct cosmology should bisect these
Clearly the data are remarkably consistent with the Doppler model; all the median values are within one standard deviation, and several are nearly centered on the predicted curve itself. None of the data are within one standard deviation of the ΛCDM curve. Given the scatter in the data and the uncertainty of the median size of a typical galaxy in magnitude-limited surveys, the tired light model cannot be eliminated on the basis of these observations.
These angular diameter observations are particularly useful because of the drastic difference between the predicted sizes based on ΛCDM expansion versus Doppler motion. And these differences grow wider with increasing redshift. At a redshift of 15, the angular size prediction of the Doppler model is 6.6 times smaller than that of the ΛCDM model. At a redshift of 20, the ratio goes up to 8.3.
This is mainly due to the increase of the angular size predicted by ΛCDM model; in the Doppler model, the angular size at high redshifts drops only slightly with increasing distance.
We therefore predict that future JWST observations of higher redshift galaxies will have a typical angular diameter of approximately 0.2 arcseconds. Astronomers who assume the ΛCDM model must assume that distant galaxies are genuinely 5–10 times smaller than nearby ones.
We can also compare the apparent brightnesses of galaxies as a function of redshift since the ΛCDM model makes different predictions than the Doppler model.
We can also compare the apparent brightnesses of galaxies as a function of redshift since the ΛCDM model makes different predictions than the Doppler model.
This is less determinative than the angular diameter test because
(1) luminosity surveys are highly sensitive to selection biases, filters, and k-corrections, and
(2) the predictions between the two models are not as disparate as with angular size predictions. As an example of the latter point, at a redshift of 13, the ratio of angular size predictions between the two models is 5.9, but the ratio of luminosity predictions is only 2.5. Galaxy brightnesses are often reported in the magnitude system in which an increase of 1 magnitude corresponds to a drop in luminosity by a factor of the fifth root of 100 (~2.51188).
--Thus, a galaxy at a redshift of 13 will appear one magnitude higher (thus fainter) under the Doppler model than under the ΛCDM model. This effect is small given the scatter in the data, but it is potentially detectable.
Most surveys of distant galaxies in JWST deep fields report the estimated absolute magnitude (indicative of its actual brightness as if it were a point source only 10 parsecs away) of the galaxy, based on the ΛCDM luminosity distance. If the Doppler model is correct, then these estimates are too faint by about one magnitude as they approach a redshift of 13. Therefore, assuming distant galaxies are truly comparable to nearby ones, we should see a slight drop in their estimated absolute magnitudes with increasing redshifts as reported in studies that assume the ΛCDM model.
Consider an extremely bright galaxy with absolute magnitude –23. If the ΛCDM model is correct, and if distant galaxies are like nearby ones, then the brightest galaxies at all redshifts should also have an estimated magnitude of around –23 as indicated by the red line.
Most surveys of distant galaxies in JWST deep fields report the estimated absolute magnitude (indicative of its actual brightness as if it were a point source only 10 parsecs away) of the galaxy, based on the ΛCDM luminosity distance. If the Doppler model is correct, then these estimates are too faint by about one magnitude as they approach a redshift of 13. Therefore, assuming distant galaxies are truly comparable to nearby ones, we should see a slight drop in their estimated absolute magnitudes with increasing redshifts as reported in studies that assume the ΛCDM model.
Consider an extremely bright galaxy with absolute magnitude –23. If the ΛCDM model is correct, and if distant galaxies are like nearby ones, then the brightest galaxies at all redshifts should also have an estimated magnitude of around –23 as indicated by the red line.
On the other hand, if the Doppler model is correct, then when the absolute magnitude of high redshift galaxies is computed by astronomers who assume the ΛCDM model, the estimates should be 2.5 times fainter (1 magnitude) for redshifts of 13. This is indicated by the black curve. The estimated absolute magnitudes of galaxies from several studies are plotted. All these studies assumed the ΛCDM model, and indeed there seems to be an overall downward trend with increasing redshift.
When we examine the estimates by Trujillo et al. on the left, we see a clear example of the Malmquist bias. The faintest galaxies (absolute magnitude ~–18) are only detected at very low redshift/distance.
When we examine the estimates by Trujillo et al. on the left, we see a clear example of the Malmquist bias. The faintest galaxies (absolute magnitude ~–18) are only detected at very low redshift/distance.
By a redshift of 2, only galaxies brighter than absolute magnitude –20 are detected. The fainter galaxies are missing in the plot—not because they are not present but because they are not easy to detect at that distance.
The brightest galaxies in that study tend to be found at the highest distances because larger distances sample a greater volume in space, increasing the probability of detecting a rare, ultra-bright galaxy, and because only bright galaxies could be seen at such a distance. 
Thus, within any given magnitude-limited survey, we expect to see a trend of increasing brightness with distance due to these selection biases. But between surveys we expect to see a downward trend if the Doppler model is correct and no trend at all if the ΛCDM model is correct. We again bin the data, this time selecting the brightest galaxy in each redshift bin to reduce selection effects. A linear least-squares fit to these data points (shown in light blue) confirms a downward trend with a slope (0.096 ± 0.038) comparable to what is expected by the Doppler model (~0.067). Thus, galaxies at high redshift do indeed appear fainter than predicted by the ΛCDM model, and by approximately the difference the Doppler model predicts."
AIG