Expanding Universe vs. Tired-Light Universe: the Rate of Energy Attenuation and the Cosmological Distance

 

Expanding Universe vs. Tired-Light Universe: the Rate of Energy Attenuation and the Cosmological Distance 

Pavle I. Premović

Laboratory for Geochemistry, Cosmochemistry&Astrochemistry,

University of Niš, pavleipremvic@yahoo.com, Niš, Serbia

The tired-light theory for the origin of the cosmological redshifts (z) is still considered a possible alternative to the expanding Universe. According to this theory, space is Euclidean, static, slowly evolving, and probably infinite {1}. The tired-light theory claims that the light of nearby or distant galaxies[1] is redshifted because it loses energy as it passes through intergalactic space. The tired-light model specifies that a photon loses energy during its journey through intergalactic space as

 E_d = E₀e^-βd

This implies that the photon wavelength λ_D should increase exponentially with the distance D as

 λ_D/λ_{0 =} e^βD

where λ₀ is the wavelength of the photon at the time of emission. Subtracting 1 from both sides of this expression and after a bit of algebra we arrive at

1 + z = e^βD

where z is the cosmological redshift of the nearby or distant galaxy light reaching the Earth.

Hence then we find

β = ln(1 + z)/D     ... (2)

or

D = ln(1 + z)/β    ... (3).

As one of the direct distance measurement methods, the “megamaser” method has demonstrated its capability for precise distance measurement of nearby galaxies. It appears this method is suitable for very few of these galaxies - “megamaser” galaxies. For the present case, we select five of these galaxies whose redshift z and distance D from the Earth (determined by this method) are known (Table 1) and their peculiar motion is negligible.

Table 1. “Megamaser” galaxies with their z, D {for details see {4} and β values.

Name of galaxy	Redshift z	D (Gly)]1	β (Gly)-1*
NGC 1052	0.004930	0.065	0.076
UGC 3789	0.010679	0.162	0.065
NGC 6323	0.02592	0.349	0.073
NGC 5765B	0.02754	0.411	0.066
NGC 6264	0.03384	0.447	0.074

                                                            *Calculated using eqn. (2).

Plugging into eqn. (2) given the above z and D, we calculated the energy attenuation coefficients (β) corresponding to these galaxies, Table 1. Their arithmetic mean is β = 0.071 (Gly)^-1.

Eqn. (3) allows us the distances between the Earth and distant galaxies if we know their light redshifts.

Table 2 gives the calculated values of D for selected distant galaxies including the above

nearby “megamaser” galaxies.

Table 2. Selected distant and “megamaser” galaxies and their z^*, D^a and D_Ned^b.

Name of galaxy	z	D(Gly)	DNed (Gly)
HD1	13.27	37	33
GN-z11	11.09	35	32
MACS0647-JD	10.7	35	31.5
EGS-zs8-1	7.73	30.5	29
HCM-6A	6.56	28.5	28
RD1	5.34	26	26
APM 08279+5255	3.91	22	23
A1689B11	2.54	18	19
NGC 6264	0.03384c	0.5	0.5
NGC 5765B	0.02754c	0.4	0.4
NGC 6323	0.02592c	0.4	0.35
UGC 3789	0.010679c	0.15	0.15
NGC 1052	0.004930c	0.07	0.07

*Wikipedia data. ^aCalculated using eqn. (3), ^bcalculated using Ned Wright's cosmological calculator and ^csee Table 1

Table 2 also gives the values of the comoving radial distance D_Ned calculated using Ned Wright's cosmological calculator assuming a flat Universe with matter density parameter Ω_m = 0.27, a vacuum energy (or dark energy) parameter Ω_Λ = 0.73, and a Hubble constant H₀ = 72 km sec^-1. What is surprising is that these values ​​based on the standard expanding model of the Universe are comparable to the values ​​for D based on the tired-light static model of the Universe. This compatibility is not a coincidence. Then a question arises: what does it imply?

HD1 (and HD2)[1] is one of the earliest and most distant known galaxies yet identified in the observable Universe. The galaxy, with an estimated redshift of about z = 13.27. Introducing into eqn. (3) this value for z and β = 0.071 (Gly)^-1 we find that the distance of the DG1 to the Earth is about 37 Gly, Table 2. The tired-light redshift model predicts about 2.7 times greater distance between the Earth and HD1 than the Hubble distance (≈ 14 Gly) or 2.7 times longer the age of this galaxy than the Hubble time (≈ 14 Gy). See below.

Using eqn. (1), we calculated that the photons of the light emitted by HD1 and reaching the Earth would lose about 93 % of its initial energy. Moreover, applying the same equation, we calculated that photons emitted from the galaxy at a distance of about 97 Gly from the Earth would lose 99 % of their initial energy.

If β^-1 >> D, then within the Hubble law β = H₀/c

H₀ = βc   … (4)

where H₀ is the Hubble constant[1] and c (= 299792 km sec^-1) is the speed of light {5}. Employing this formula, H₀ = 72 km sec^-1 (Mpc)^-1 and a given value of c, we found β ≈ 0.073 (Gly)^-1.

The Hubble distance, as a unit of distance in cosmology, is defined as c/H₀ - the speed of light multiplied by the Hubble time. It is equivalent to 13.7 Gly. By definition, the numerical value of the Hubble distance in light years is, equal to that of the Hubble time in years (roughly the age of the Universe A_U) or

(t_H =) A_U = 1/H₀    … (5).

Combining eqns. (4) and (5), we find that the age of the Universe A_U = 1/βc. Introducing into this formula given values of β and c, we get A_U = 1/βc ≈ (1/0.071) Gy ≈ 14 Gy. This value is consistent to the accepted current value for the Hubble time of around 14 Gy.

References

[1] P. A. LaViolette, Genesis of the Cosmos. The ancient science of continuous creation. Bear & Company (2004).

[2] P. I. Premović, Distant galaxies in the non-expanding (Euclidean) Universe: the light speed redshift. The General Science Journal, December 2021.

[3] P. I. Premović, The tired-light hypothesis: derivation of basic relations. The General Science Journal, November 2022.

[4] P. I. Premović, The age of the “megamaser” galaxies in the Big Bang Universe. The General Science Journal, December 2021.

[5] P. A. LaViolete, Is the Universe really expanding? ApJ. 301, 544-553 (1986).

[6] N. Jackson, The Hubble constant, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5253801/.

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[1] We define nearby galaxies as those whose redshift z is from 0.001 to 0.1 (or 0.001 ≤ z ≤ 0.1) and distant galaxies with z > 0.1 [2]. Of course, there is no sharp line between nearby and distant galaxies.

[2] A simple derivation of this equation is given in {3}.

[3] They do not exist anymore.

[4] Recent values of H₀ are in the range of about 67 – 74 km sec^-1 (Mpc)^-1 {6}.