New research suggests that our universe has no dark matter | About us

A leading theoretical physicist has questioned whether dark matter really exists.

Dark Matter is a placeholder for what appears to be mass without substance which suffuses the universe, observable only by the gravity it exerts and thought by mainstream cosmologists to account for 27% of the matter in the universe with 'ordinary' matter making up just 5%. The rest - 68% - being composed of dark energy, another placeholder for something theory says should be there to account for the expansion of the universe, but which we don't have a model for in the standard model of particles and related fields.

I don't pretend to understand this stuff, but I'll post it here by way of a rebuttal of creationist claims that scientists devise experiments to try to prove preconceptions and that peer-review is just to ensure conformity to scientific orthodoxy.

Besides, the HTML coding is the sort of challenge I enjoy.

In fact, science is about continued reassessment and revision with names made not by confirming preconceptions but by overthrowing established consensus or exposing flaws in it which require further investigation. The leading theoretical physicist is Professor Rajendra Gupta of the Faculty of Science, University of Ottawa, Canada, who has just published a paper in

*The Astrophysical Journal*. He has also authored an earlier paper which he believes shows the Universe to be about twice as old as the mainstream consensus believes it to be, so he can hardly be described as subscribing to some establishment orthodoxy. His work is explained in a University of Ottawa News release:

The current theoretical model for the composition of the universe is that it’s made of ‘normal matter,’ ‘dark energy’ and ‘dark matter.’ A new uOttawa study challenges this.The following extract from his open access paper is highly mathematical, so if you can understand it, you're better at higher maths than I could ever hope to be:

A University of Ottawa study published today challenges the current model of the universe by showing that, in fact, it has no room for dark matter.

In cosmology, the term “dark matter” describes all that appears not to interact with light or the electromagnetic field, or that can only be explained through gravitational force. We can’t see it, nor do we know what it’s made of, but it helps us understand how galaxies, planets and stars behave.

Rajendra Gupta, a physics professor at the Faculty of Science, used a combination of the covarying coupling constants (CCC) and “tired light” (TL) theories (the CCC+TL model) to reach this conclusion. This model combines two ideas — about how the forces of nature decrease over cosmic time and about light losing energy when it travels a long distance. It’s been tested and has been shown to match up with several observations, such as about how galaxies are spread out and how light from the early universe has evolved.

This discovery challenges the prevailing understanding of the universe, which suggests that roughly 27% of it is composed of dark matter and less than 5% of ordinary matter, remaining being the dark energy.

Challenging the need for dark matter in the universe

“Redshifts” refer to when light is shifted toward the red part of the spectrum. The researcher analyzed data from recent papers on the distribution of galaxies at low redshifts and the angular size of the sound horizon in the literature at high redshift. By challenging the need for dark matter in the universe and providing evidence for a new cosmological model, this study opens up new avenues for exploring the fundamental properties of the universe. The study, Testing CCC+TL Cosmology with Observed Baryon Acoustic Oscillation, was published in the peer-reviewed Astrophysical Journal.The study's findings confirm that our previous work (“JWST early Universe observations and ΛCDM”) about the age of the universe being 26.7 billionyears has allowed us to discover that the universe does not require dark matter to exist. In standard cosmology, the accelerated expansion of the universe is said to be caused by dark energy but is in fact due to the weakening forces of nature as it expands, not due to dark energy.

There are several papers that question the existence of dark matter, but mine is the first one, to my knowledge, that eliminates its cosmological existence while being consistent with key cosmological observations that we have had time to confirm.

Professor Rajendra Gupta

Faculty of Science

University of Ottawa, Canada.

AbstractThe point here is not to bamboozle anyone with (to me) incomprehensible maths, but to demonstrate the lie in the creationist claim that scientists design experiments to confirm preconceptions or to deliver paid-for results, and that the peer-review process is to ensure conformity to establishment dogma.

The primary purpose of this paper is to see how well a recently proposed new model fits (a) the position of the baryon acoustic oscillation (BAO) features observed in the large-scale distribution of galaxies and (b) the angular size measured for the sound horizon due to BAO imprinted in the cosmic microwave background (CMB) anisotropy. The new model is a hybrid model that combines the tired light (TL) theory with a variant of the ΛCDM model in which the cosmological constant is replaced with a covarying coupling constants' (CCC) parameter α. This model, dubbed the CCC+TL model, can fit the Type Ia supernovae Pantheon+ data as accurately as the ΛCDM model, and also fit the angular size of cosmic dawn galaxies observed by the James Webb Space Telescope, which is in tension with the ΛCDM model. The results we obtained are 151.0 (±5.1) Mpc for the absolute BAO scale at the current epoch, and the angular size of the sound horizon θ_{sh}= 0°60, matching Planck's observations at the surface of the last scattering when the baryon density is set to 100% of the matter density and ∣α∣ is increased by 5.6%. It remains to be seen if the new model is consistent with the CMB power spectrum, the Big Bang nucleosynthesis of light elements, and other critical observations.

1. Introduction

One of the most important tests of a cosmological model is to reproduce in the galaxy distribution the signatures of the baryon acoustic oscillations (BAOs) resulting from the sound waves in the baryon–photon fluid at the time when photons and baryon decoupled, and radiation traveled freely in space. This radiation is observed as the cosmic microwave background (CMB). The BAO features are detected as tiny temperature fluctuations (anisotropies) in the highly isotropic CMB observations. These oscillations are believed to develop into large-scale structures as higher-density regions of perturbations become the nucleation points where galaxies form. Thus, the two features are expected to be correlated, and BAO could serve as a fundamental standard ruler to test cosmological models (Peebles & Yu 1970; Bond & Efstathiou 1984; Eisenstein & Hu 1998; Meiksin et al. 1999). The observation of BAO features at different redshifts endorses the propagation of primordial gravitational instability (Cole et al. 2005; Eisenstein et al. 2005.1; Fronenberg et al. 2023). Xu et al. (2023.1) have recently established evidence for BAOs from galaxy–ellipticity correlations. Tully et al. (2023.2) have presented remarkably strong evidence for the existence of an individual BAO signal atz= 0.068. Shao et al. (2023.48) raised the possibility of using the angular scale of cosmic inhomogeneities as a new, model-independent way to constrain cosmological parameters.

Sutherland (2012) succinctly stated, "...the observed BAO features support the standard cosmology in several independent ways: the existence of features supports the basic gravitational instability paradigm for structure formation; the relative weakness of the BAO feature supports the ∼1:5 ratio of baryons to dark matter, since baryon-dominated universe would have a BAO feature much stronger than observed; and the observed length-scale of the feature in redshift space is consistent with the concordance ΛCDM model derived from the CMB and other observations, with Ω_{m}≈ 0.27 and H_{0}≈ 70 km s^{−1}Mpc^{−1}(Komatsu et al. 2011)."

Weinberg et al. (2013) have shown that BAO features in the matter power spectrum (galaxies), when combined with the tracer power spectrum (CMB), can effectively constrain the cosmological parameter and test a model. For our purpose, we are interested in the BAO measurements of angular separations θBAO of pairs of galaxies at different redshift values. Carvalho et al. (2016) used 409,337 luminous red galaxies in the redshift rangez= [0.440, 0.555] to estimate θ_{BAO}(z) at six redshift shells. Their work was extended to include observations that provided θ_{BAO}atz= 0.11 withinz= [0.105, 0.115] (Carvalho et al. 2021), and at up toz= 0.65 (Lemos et al. 2023.3). We will use their data to explore if the recently proposed hybrid model (Gupta 2023.4) is consistent with features of the BAOs observed in the CMB and matter power spectra. This model comprises a modified ΛCDM model permitting the covariation of coupling constants (CCC) and includes the tired light (TL) phenomenon to partially account for the observed redshift. This two-parameter hybrid model, dubbed CCC+TL, was able to account for the bewildering observation by the James Webb Space Telescope (JWST) showing unexpected morphology of galaxies existent at cosmic dawn. The model parameters H_{0}andα, the latter determining the strength of the coupling constants' variation and replaces Λ of the standard model, are determined by fitting the Type Ia supernovae (Pantheon+) data (Brout et al. 2022; Scolnic et al. 2022.1).

The galaxies observed in the early Universe, some less than 500 million years after the Big Bang, appear to have shapes, structures, and masses similar to those in existence for billions of years (e.g., Naidu et al. 2022.2a, 2022.3b; Curtis-Lake et al. 2023.5; Hainline et al. 2023.6; Labbé et al. 2023.7; Robertson et al. 2023.8) but with angular sizes 1 order of magnitude smaller than expected for such galaxies (e.g., Finkelstein et al. 2022.4; Naidu et al. 2022.2a, 2022.3b; Yang et al. 2022.7; Adams et al. 2023.9; Atek et al. 2023.10b; Austin et al. 2023.11; Baggen et al. 2023.12; Chen et al. 2023.13b; Donnan et al. 2023.14; Ono et al. 2023.15; Tacchella et al. 2023.16a, 2023.17b; Wu et al. 2023.18). Attempts have been made to resolve the problem by modifying the star and galaxy formation models (e.g., Haslbauer et al. 2022.8; Inayoshi et al. 2022.9; Atek et al. 2023.19a; Kannan et al. 2023.20; Keller et al. 2023.21; Mason et al. 2023.22; McCaffrey et al. 2023.23; Mirocha & Furlanetto 2023.24; Regan 2023.25; Whitler et al. 2023.26a, 2023.27b; Yajima et al. 2023.28), such as by compressing time for the formation of Population III stars and galaxies more and more by considering the presence of primordial massive black hole seeds, and super-Eddington accretion rates in the early Universe (Ellis 2022.10; Larson et al. 2022.11; Brummel-Smith et al. 2023.29; Chantavat et al. 2023.30; Dolgov 2023.31; Maiolino et al. 2023.32; Reinoso et al. 2023.33). Other researchers (Boyett et al. 2023.34; Bunker et al. 2023.35; Dekel et al. 2023.36; Eilers et al. 2023.37; Haro et al. 2023.38; Long et al. 2023.39; Looser et al. 2023.40) are concerned if they provide satisfactory answers. Some even suggest looking for new physics (Chen et al. 2023.41a; Mauerhofer & Dayal 2023.42; Schneider et al. 2023.43). In the words of Garaldi et al. (2023.44), "Cosmological simulations serve as invaluable tools for understanding the Universe. However, the technical complexity and substantial computational resources required to generate such simulations often limit their accessibility within the broader research community. Notable exceptions exist, but most are not suited for simultaneously studying the physics of galaxy formation and cosmic reionization during the first billion years of cosmic history." According to Xiao et al. (2023.45), "Massive optically dark galaxies unveiled by JWST challenge galaxy formation models." (See also Greene et al. 2023.46; Katz et al. 2023.47; Ormerod et al. 2024.)

The CCC+TL model predicts the age of the Universe as 26.7 Gyr against the generally accepted value of 13.8 Gyr. This is of deep concern and needs the model validation against multiple observations, including BAOs, CMB, Big Bang nucleosynthesis (BBN), and globular cluster ages. Our focus here is on BAOs. This paper is organized to include the theoretical background in Section 2, results in Section 3, discussion in Section 4, and conclusions in Section 5.

2. Theoretical Background

CCC Model. The modified FLRW metric, incorporating the covarying coupling constant (CCC) concept, is (Gupta 2023.4) 1 $$\begin{array}{}\text{(1)}& \begin{array}{r}\begin{array}{rcl}{ds}^{2}& =& {c}_{0}^{2}{dt}^{2}f{\left(t\right)}^{2}-a{(t)}^{2}f{\left(t\right)}^{2}\\ & & \times \left({\displaystyle \frac{{dr}^{2}}{1-{kr}^{2}}+{r}^{2}(d{\theta}^{2}+{\mathrm{sin}}^{2}\theta d{\varphi}^{2})}\right),\end{array}\end{array}\end{array}$$ the Friedmann equations are

$$\begin{array}{}\text{(2)}& \begin{array}{rcl}& & {\left({\displaystyle \frac{\dot{a}}{a}+\alpha}\right)}^{2}={\displaystyle \frac{8\pi {G}_{0}}{3{c}_{0}^{2}}\epsilon -{\displaystyle \frac{{kc}_{0}^{2}}{{a}^{2}},\mathrm{and}}}\end{array}\end{array}$$ $$\begin{array}{}\text{(3)}& \begin{array}{rcl}& & {\displaystyle \frac{\ddot{a}}{a}=-{\displaystyle \frac{4\pi {G}_{0}}{3{c}_{0}^{2}}(\epsilon +3p)-\alpha \left({\displaystyle \frac{\dot{a}}{a}}\right),}}\end{array}\end{array}$$ and the continuity equation is

$$\begin{array}{}\text{(4)}& \begin{array}{rcl}& & \dot{\epsilon}+3{\displaystyle \frac{\dot{a}}{a}(\epsilon +p)=-\alpha (\epsilon +3p).}\end{array}\end{array}$$

Here $a$ is the scale factor, G_{0}is the current value of the gravitational constant, c_{0}is the current value of the speed of light,kis the curvature constant,αis a constant defining the variation of the constant through a function $f(t)=\mathrm{exp}\left(\alpha (t-{t}_{0})\right)$ with time measured from the beginning of the Universe and t_{0}the current time,εis the energy density of all the components, andpis their pressure. Using the functionf(t), c(t) = cand_{0}f(t)G = Gin the CCC model. The solutions of this Equation (4) for matter (_{0}f(t)^{3}p= 0) and radiation (p =ε/3) are, respectively, $$\begin{array}{}\text{(5)}& \begin{array}{rcl}& & {\epsilon}_{m}={\epsilon}_{m,0}{a}^{-3}{f}^{-1},\mathrm{and}\text{}{\epsilon}_{r}={\epsilon}_{r,0}{a}^{-4}{f}^{-2}.\end{array}\end{array}$$ Defining the Hubble expansion parameter as $H=\dot{a}/a$ , we may write Equation (2) for a flat Universe (k= 0) as

$$\begin{array}{}\text{(6)}& \begin{array}{rcl}& & {(H+\alpha )}^{2}={\displaystyle \frac{8\pi {G}_{0}}{3{c}_{0}^{2}}\epsilon \Rightarrow {\epsilon}_{c,0}\equiv {\displaystyle \frac{3{c}_{0}^{2}{({H}_{0}+\alpha )}^{2}}{8\pi {G}_{0}}.}}\end{array}\end{array}$$ This equation defines the critical density of the Universe in the CCC model. Using Equations (5) and (6), we may write

$$\begin{array}{}\text{(7)}& \begin{array}{rcl}& & H=({H}_{0}+\alpha ){({\mathrm{\Omega}}_{m,0}{a}^{-3}{f}^{-1}+{\mathrm{\Omega}}_{r,0}{a}^{-4}{f}^{-2})}^{1/2}-\alpha .\end{array}\end{array}$$ In this equation, relative matter density Ω_{m,0}= ε_{m,0}/ε_{c,0}and relative radiation density Ω_{r,0}= ε_{r,0}/ε_{c,0}. Since Ω_{r,0}≪ Ω_{m,0}, and we do not have to worry about the dark energy density in the CCC model, Equation (7) simplifies to

$$\begin{array}{}\text{(8)}& \begin{array}{rcl}& & H=({H}_{0}+\alpha ){({a}^{-3}{f}^{-1}+{\mathrm{\Omega}}_{r,0}{a}^{-4}{f}^{-2})}^{1/2}-\alpha .\end{array}\end{array}$$ Since the observations are made using redshiftz, we have to see how the scale factor $a$ relates tozin the CCC model. Along the spatial geodesic (θandϕconstant) between the observer and the source at a fixed timetusing the modified FLRW metric (Equation (1))

$$\begin{array}{}\text{(9)}& \begin{array}{rcl}& & ds=a(t)f(t)dr.\end{array}\end{array}$$ Thus, the proper distance for commoving coordinater(since $a\left({t}_{0}\right)\equiv 1=f\left({t}_{0}\right)$) $$\begin{array}{}\text{(10)}& \begin{array}{rcl}& & {d}_{p}=a(t)f(t){\int}_{0}^{r}dr=a(t)f(t)r\Rightarrow {d}_{p}\left({t}_{0}\right)=r.\end{array}\end{array}$$

Since light follows the null geodesic, Equation (1) yields for a light emitted by a source at a time t_{e}and detected by the observer at a time t_{0}

$$\begin{array}{}\text{(11)}& \begin{array}{rcl}& & {c}_{0}{\int}_{{t}_{e}}^{{t}_{0}}{\displaystyle \frac{dt}{a(t)}={\int}_{0}^{r}dr=r={d}_{p}({t}_{0}).}\end{array}\end{array}$$

It can now be easily shown (e.g., Ryden 2017) thata= 1/(1 +z), i.e., the same as for the ΛCDM model.

We now need to transposef(t)tof(z), as it is the latter that we will require in calculating the proper distance. Following Gupta's (2023.4) Equations (24)–(27), we have

$$\begin{array}{}\text{(12)}& \begin{array}{rcl}& & \begin{array}{c}{f}^{-1/2}=x={(-{\displaystyle \frac{D}{2A}+{({(-{\displaystyle \frac{D}{2A}})}^{2}+{\left({\displaystyle \frac{C}{3A}}\right)}^{3})}^{1/2}})}^{1/3}\\ +{\textstyle \phantom{\rule{0.167em}{0ex}}}{(-{\displaystyle \frac{D}{2A}-{({(-{\displaystyle \frac{D}{2A}})}^{2}+{\left({\displaystyle \frac{C}{3A}}\right)}^{3})}^{1/2}})}^{1/3},\mathrm{where}\\ A=1-{\displaystyle \frac{3}{2}{\displaystyle \frac{({H}_{0}+\alpha )}{\alpha}=1-C,}}\\ D=-{a}^{3/2},\mathrm{and}\text{}x=\mathrm{exp}(-{\displaystyle \frac{\alpha (t-{t}_{0})}{2}}).\end{array}\end{array}\end{array}$$

Since the scale factor $a$ = 1/(1 +z), we have D = −[1/(1 +z)]^{3/2}. Thus, the above equation provides the functionf(for the matter-dominated Universe. What about its expression in the radiation-dominated Universe? Sincez, H_{0}, α)z≫ 1 in such a Universe, i.e.,t≪ t_{0}, it is easy to see that $f(t)=\mathrm{exp}\left(\alpha (t-{t}_{0})\right)$ approaches a constant value. We can, therefore, use the same expression forf(z), i.e., Equation (12) for all values ofz. We now need the expression for the proper distance d_{p}. Since $dt=dt\times da/da=da/\dot{a}$ , we may write Equation (10)

$$\begin{array}{}\text{(13)}& \begin{array}{rcl}& & {d}_{p}\left({t}_{0}\right)={c}_{0}{\int}_{{t}_{e}}^{{t}_{0}}{\displaystyle \frac{dt}{a(t)}={c}_{0}{\int}_{{a}_{e}}^{1}{\displaystyle \frac{da}{a\dot{a}}={c}_{0}{\int}_{{a}_{e}}^{1}{\displaystyle \frac{da}{{a}^{2}H},}}}\end{array}\end{array}$$

and sincea= 1/(1 +z),da = − dz/(1 + z), we get, using Equation (8),^{2}= −dza^{2}

$$\begin{array}{}\text{(14)}& \begin{array}{rcl}& & \begin{array}{c}{d}_{p}\left({t}_{0}\right)={c}_{0}{\int}_{0}^{z}{\displaystyle \frac{dz}{H}={c}_{0}{\int}_{0}^{z}}\\ \times {\textstyle \phantom{\rule{0.167em}{0ex}}}{\displaystyle \frac{dz}{({H}_{0}+\alpha ){({(1+z)}^{3}{f}^{-1}+{\mathrm{\Omega}}_{r,0}{(1+z)}^{4}{f}^{-2})}^{1/2}-\alpha}.}\end{array}\end{array}\end{array}$$

We can now follow TL and CCC+TL models developed by Gupta (2023) for our computations in this work.Sound Horizon Distance and Angular Size.Denoted as d_{sh}(t_{ls}), it represents the distance sound travels at the speed c_{s}(t) in the photon–baryon fluid from the Big Bang until such plasma cools down and disappears due to the formation of atoms, i.e., until the time of last scatteringtcorresponding to the redshift_{ls}z. One may write the sound horizon distance (Durrer 2021.2), using the metric given by Equation (1) for the CCC+TL model, as_{ls}

$$\begin{array}{}\text{(15)}& \begin{array}{rcl}& & {d}_{\mathrm{sh}}\left({t}_{\mathrm{ls}}\right)=a({t}_{\mathrm{ls}})f({t}_{\mathrm{ls}}){\int}_{0}^{{t}_{\mathrm{ls}}}{\displaystyle \frac{{c}_{s}(t)dt}{a(t)}.}\end{array}\end{array}$$

The speed of sound in terms of the speed of light is given by (Durrer 2021)

$$\begin{array}{}\text{(16)}& \begin{array}{r}\begin{array}{rcl}{c}_{s}(t)& \approx & {\displaystyle \frac{{c}_{0}}{\sqrt{3}}{(1+{\displaystyle \frac{3{\mathrm{\Omega}}_{b}}{4{\mathrm{\Omega}}_{r}}})}^{-1/2}}\\ & =& {\displaystyle \frac{{c}_{0}}{\sqrt{3}}{(1+{\displaystyle \frac{3{\mathrm{\Omega}}_{b,0}}{4{\mathrm{\Omega}}_{r,0}}a(t)f(t)})}^{-1/2},\mathrm{or}}\end{array}\end{array}\end{array}$$

$$\begin{array}{}\text{(17)}& \begin{array}{rcl}& & {c}_{s}(z)\approx {\displaystyle \frac{{c}_{0}}{\sqrt{3}}{(1+{\displaystyle \frac{3{\mathrm{\Omega}}_{b,0}f(z)}{4{\mathrm{\Omega}}_{r,0}(1+z)}})}^{-1/2},}\end{array}\end{array}$$

where Ω_{b}is the baryon density and Ω_{r}is the radiation density. Following Equations (13) and (14), we get

$$\begin{array}{}\text{(18)}& \begin{array}{rcl}& & \begin{array}{c}{d}_{\mathrm{sh}}\left({z}_{\mathrm{ls}}\right)={\displaystyle \frac{1}{1+{z}_{\mathrm{ls}}}{\int}_{\mathrm{\infty}}^{{z}_{\mathrm{ls}}}}\\ \times {\textstyle \phantom{\rule{0.167em}{0ex}}}{\displaystyle \frac{{c}_{s}(z)dz}{({H}_{c}+\alpha ){({(1+z)}^{3}{f}^{-1}+{\mathrm{\Omega}}_{r,0}{(1+z)}^{4}{f}^{-2})}^{1/2}-\alpha}.}\end{array}\end{array}\end{array}$$

It is to be noted that the variation of the speed of light is already included in the Friedmann equations and all the expressions derived from it. In addition, we have droppedf(tin Equation (18), since we are observing dsh in today's distance unit when_{ls})f= 1. Next, we have to determinezin the CCC+TL model wherein the constants evolve as_{ls}c(t) = c, and_{0}f(t), G = G_{0}f(t)^{3}, h = h_{0}f(t)^{2}k, and distance is measured using the speed of light (Gupta 2022.12a). How does the CMB Planck spectrum evolve with the redshift? We know that the frequency evolves as_{B}= k_{B,0}f(t)^{2}ν = ν, and volume_{0}(1 + z), d ν = d ν_{0}(1 + z)Vevolves as

$$\begin{array}{}\text{(19)}& \begin{array}{r}\begin{array}{rcl}V& =& {V}_{0}a{\left({z}_{c}\right)}^{3}f{\left({z}_{c}\right)}^{3}={V}_{0}{(1+{z}_{c})}^{-3}f{\left({z}_{c}\right)}^{3}\\ & =& {V}_{0}{(1+z)}^{-3}f{\left({z}_{c}\right)}^{3}{(1+{z}_{t})}^{3},\end{array}\end{array}\end{array}$$

since $1+z=(1+{z}_{c})(1+{z}_{t})$ . The energy density of the CMB photons in the frequency rangeνandν + d ν, assuming it has the Planck spectrum, is given by

$$\begin{array}{}\text{(20)}& \begin{array}{rcl}& & {u}_{\nu}d\nu \equiv {\displaystyle \frac{8\pi {\nu}^{2}\text{}h\nu \text{}d\nu}{{c}^{3}\phantom{\rule{0ex}{2.5ex}}[\mathrm{exp}\left({\textstyle \frac{h\nu}{{k}_{B}T}}\right)-1\phantom{\rule{0ex}{2.5ex}}]}.}\end{array}\end{array}$$

Therefore, the number density of photons

$$\begin{array}{}\text{(21)}& \begin{array}{rcl}& & {n}_{\nu}={\displaystyle \frac{{u}_{\nu}d\nu}{h\nu}={\displaystyle \frac{8\pi \text{}{\nu}^{2}\text{}d\nu}{{c}^{3}\phantom{\rule{0ex}{2.5ex}}[\mathrm{exp}\left({\textstyle \frac{h\nu}{{k}_{B}T}}\right)-1\phantom{\rule{0ex}{2.5ex}}]}.}}\end{array}\end{array}$$

The number of photons in a volumeVis conserved, i.e.,

$$\begin{array}{}\text{(22)}& \begin{array}{r}\begin{array}{rcl}{n}_{\nu}V& =& {n}_{{\nu}_{0}}{V}_{0}\Rightarrow {n}_{\nu}{V}_{0}{(1+z)}^{-3}f{\left({z}_{c}\right)}^{3}{(1+{z}_{t})}^{3}={n}_{{\nu}_{0}}{V}_{0},\mathrm{or}\\ {n}_{\nu}& =& {n}_{{\nu}_{0}}{(1+z)}^{3}f{\left({z}_{c}\right)}^{-3}{(1+{z}_{t})}^{-3}.\end{array}\end{array}\end{array}$$

We may now write

$$\begin{array}{}\text{(23)}& \begin{array}{r}\begin{array}{rcl}{n}_{\nu}& =& {\displaystyle \frac{8\pi {\nu}_{0}^{2}\text{}d{\nu}_{0}}{{c}_{0}^{3}[\mathrm{exp}\left({h}_{0}{\nu}_{0}/{k}_{B,0}{T}_{0}\right)-1]}{(1+z)}^{3}{f}^{-3}{(1+{z}_{t})}^{-3},}\\ & =& {\displaystyle \frac{8\pi \text{}{\nu}^{2}\text{}d\nu}{{c}^{3}[\mathrm{exp}\left(h\nu /{k}_{B}T\right)-1]}{(1+{z}_{t})}^{-3},}\end{array}\end{array}\end{array}$$

where T = T_{0}(1 +z). We can see that the CMB emission has the blackbody spectrum, but its intensity scales as due to the TL effect. We can now determinezin the next section._{ls}

Rajendra P. Gupta 2024

Testing CCC+TL Cosmology with Observed Baryon Acoustic Oscillation Features

ApJ96455. doi: 10.3847/1538-4357/ad1bc6

Copyright: © 2024 The authors.

Published by IOP Publishing. Open access.

Reprinted under a Creative Commons Attribution 4.0 International license (CC BY 4.0)

In fact, science thrives on challenge and questioning and peer-review, as anyone who has ever read one will testify, it to ensure that the authors have established their findings with sufficient academic rigour, have constructed properly controlled experiments and eliminated possible sources of bias. Any editor of a scientific journal would positively welcome a paper that challenges establishment consensus because it is those papers that become well known in the specialty and so attract a high number of readers and citations.

It's a characteristic of creationist frauds that they routinely accuse their opponents of things of which they themselves are guilty. The only people claiming to be scientists who deliver 'orthodox' conclusions are so-called 'creation scientists' who are required to swear an oath that they will only ever reach a particular conclusion as a condition of their employment. Any 'peer-review' of their work is to ensure compliance with that oath and conformity with creationist dogma before publication and payment.

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