Memorandum of Professor Rajendra Gupta

The following is the full open-letter memorandum of Dr. Gupta, with regards to a study published that can be found here:

JWST early Universe observations and ΛCDM cosmology 

Monthly Notices of the Royal Astronomical Society, Volume 524, Issue 3, September 2023, Pages 3385–3395,


Memorandum of October 12th, 2023: 

Subject: ‘JWST early Universe observations and ΛCDM cosmology’ – response to media criticism

I have come to know of many criticisms of my recently published paper in media.  Most appear to be due to the critics not finding time to study the paper properly.  I’ll attempt to respond to them here.

The new model has too many fitting parameters:  No, it has precisely the same number of fitting parameters, i.e., two, as the standard model.  The dark energy density parameter of the standard model has been replaced by the parameter that defines the variation of the coupling constant.  No extra parameter is required to assign tired light’s contribution to the redshift.  It is determined by equating the distance light travels in the expanding universe and tired light scenarios.

Tired light would add a “blurring effect” to distant galaxies:  I do not suggest the tired light effect be caused by the scattering process.  I believe it is due to an unknown cosmic drag on photons.  There is no blurring effect as a result.

Tired light would eliminate cosmological time dilation:  Indeed, tired light has no time dilation.  Time dilation is only due to the expanding universe proportion of the redshift, which is dominant in the hybrid mode.  I have correctly taken it into account when fitting the supernovae type 1a data and examined it in the context of high redshift quasars with no conflict.  The data fit with the new model is as good as with the standard model, showing that the new model takes time dilation appropriately into account.

Tired light fails the Tolman surface brightness test:  It is an important test as the surface brightness is modified due to time dilation caused by the expanding universe – the duration between two emitted photons is stretched when observed, reducing the flux and the luminosity.  The tired light model alone does not fit the supernovae data.  In the new model, the expansion component is dominant, and it has no tension with the surface brightness as it fits the data as accurately as the standard model.

The new model has not been shown to reproduce the baryon acoustic oscillation (BAO) features in the cosmic microwave background and galaxies’ distribution:  I have shown in a recent paper (under review by Astrophysical Journal) that the new model faithfully fits the observed angular sizes of these features.

Tired light would change the thermal, blackbody spectrum of the cosmic microwave background (CMB):  I have shown in the said paper that the thermal-blackbody spectrum remains blackbody in the new model.

The new model has not been shown to fit the CMB thermal anisotropy power spectrum:  It is an onerous task to develop a CMB code for a new model.  One of my students is working on it.  However, one essential feature of CMB is BAO, and, as discussed above, I have shown the new model to be compliant with the observed BAO features.

The age of the oldest globular clusters approximately represents the age of the universe, and none has been found to conflict with the 13.8 billion years age of the universe:  As is well known, the age of globular clusters is model-dependent, and models have been adjusted whenever the age of a star or cluster exceeds the universe’s age. Bolte and Hogan, in 1995, determined certain cluster ages to be  billion years. Considering the Methuselah star, Tang and Joyce, in 2021, revised its best age estimate from  billion years down to a comfortable  billion years by adjusting parameters in the MESA stellar evolution code. If the universe’s age is established by other methods to be significantly higher than the currently accepted 13.8 billion years, astrophysicists will be relieved from the burden of constraining stellar ages below 13.8 billion years. This is evident from the very recent work of Llorente de Andrés, who determined the age of globular cluster NGC104 between 19.04 and 20.30 billion years after learning that the universe could be 26.7 billion years old. With no age constraint to worry for recently born clusters, Jeffries and his coauthors a few months ago adjusted the age of a young open cluster IC 4665 from 32 million years to greater than 50 million years. Thus, the age of a star or a cluster cannot be considered a constraint on the universe’s age.

Observations and experiments have shown that coupling constants don’t evolve:  I have been diligently looking for experiments and observations that could detect the variation of the covarying coupling constants.  In this context, last year, I visited NIST (National Institute of Standards and Technology) in Gaithersburg, MD, and gave a talk on the subject.  In all the experiments we could imagine, the constants’ variations cancel out, including in the fine structure constant, atomic clocks in space, Oklo natural nuclear reactor, and other experiments.  Attempts have been made to check the variation of these constants independently.  However, the coupling constants’ variations are interrelated through a common function.  Fixing one constant fixes this common function and, thus, all the interrelated constants.  For example, if you wish to measure the variation of the gravitational constant G while keeping the speed of light c fixed, you will get negative results.

I have cherry-picked the data to fit the new model:  I considered Pantheon+ supernovae type 1a data not only to see how well each model fits the data but also to reliably estimate the two free parameters.  This data fit is critical for any model to qualify for further study.  I have now shown the new model’s compliance with the baryon acoustic oscillation feature observed in the microwave background and galaxies’ distribution.

The new model’s predictions:  The model predicts the cosmic dawn to shift by a factor of ten to higher redshifts.  Cosmic dawn is the period from about 50 million to one billion years after the Big Bang when the first stars, black holes, and galaxies formed. That means the nascent galaxies will not be observable until the redshift of about 100 rather than 10 predicted by the standard model.  Higher background cosmos temperature that impedes the formation of galaxies will be more than offset by the effects of covarying coupling constants and tired light.


Rajendra Gupta, Ph.D., FRAS

Adjunct Professor
Department of Physics
University of Ottawa
STEM Complex, Room 508
150 Louis-Pasteur Pvt.

Ottawa, ON, Canada K1N 6N5                                                                                  October 12, 2023