Hubble Diagram Test of SN1a Supernovae and High Redshift Gamma Ray Bursts

Laszlo Arpad Marosi

doi:doi:10.11648/j.ajaa.20251203.17

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Hubble Diagram Test of SN1a Supernovae and High Redshift Gamma Ray Bursts

Laszlo Arpad Marosi^*

Published in American Journal of Astronomy and Astrophysics (Volume 12, Issue 3)

Received: 19 June 2025 Accepted: 4 August 2025 Published: 11 September 2025

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Abstract

Hubble diagrams are examined for SN1a supernovae in the redshift range z = 0.01–1.3 and for gamma ray bursts in the range z = 0.034–8.1. It is shown that in the low redshift range, the Hubble diagram shows an innate equivocality between the ΛCDM and the tired light model. This means that the strong agreement between the z/µ data, calculated with the parameters of the ΛCDM model, and the experimentally measured z/µ values cannot be considered as definite evidence for the expansion hypothesis. The exponential function z+1 = e^{h(TL) × t(d)} which is characteristic of the tired light redshift mechanism, fits the data with similarly high accuracy. Hence, on the premise of low redshift data, a decision for or against either model is completely arbitrary. We expect that in the high RS range it should be possible to check more precisely whether the HD follows the linear H₀D/c or the exponential relation, an effect that is not perceptible in the z< 1 region. Unfortunately, SN1a supernovae data are accessible only to a limited range of distances. This constraints on the data motivated several attempts to obtain cosmological parameters from gamma ray bursts observations. GRBs are the most brilliant sources in the universe. Tey are acquired up to RSs of ~8 and higher, and endeavours are made to use GRB data to calculate HD. In this study a total of 138 calibrated, cosmology independent GRB z/μ data points collected by Liu and Wei from the 557 Union2 compilations were used as the starting data set. It is shown that the Hubble diagram for high redshift gamma ray bursts shows poor agreement with the ΛCDM model, but concurs with the exponential energy decay following from the tired light redshift hypothesis.

Published in	American Journal of Astronomy and Astrophysics (Volume 12, Issue 3)
DOI	10.11648/j.ajaa.20251203.17
Page(s)	126-134
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Distances and Redshifts, Galaxies, High-redshift, Gamma Ray Bursts, Cosmological Parameters

1. Introduction

The essential premise of Big Bang (BB) cosmology is that the universe is expanding, and Hubble's law, Hubble

[1]

, is viewed as the most persuasive proof for cosmic expansion. In present-day cosmology, the velocity interpretation of the redshift (RS) of spectral lines has achieved a dogmatic status, and objections against it have gone unobserved.

Regardless of whether this interpretation is correct or not, Hubble’s law is a RS/distance (d) relation, and an interpretation of this as a velocity is only a hypothesis. Supporting the velocity interpretation is the good agreement between the observed z/µ data for SN1a supernovae in the RS range z < ~ 1.3 with data determined based on the parameters Ώ_M, Ώ_λ, w and H₀ of the ΛCDM model, which is viewed as proof for general expansion. Despite its widespread acceptance, however, this conclusion is equivocal, and the current circumstance is fairly confounding. Based on a semiquantitative examination of SN1a data Sorell

[2]

reported that in the low-RS range, the Hubble diagram (HD) for a tired light (TL) cosmology gives good agreement with the Type Ia supernova data. A detailed examination of mixed SN1a and gamma ray burst (GRB) data Marosi

[3]

has also shown that in the RS range 0.031–8.1, the TL model, Zwicky

[4]

, closely fits the experimental data, while the ΛCDM model is in poor agreement with observation. A comparable outcome was described by Traunmüller

[5]

, whose examination of 892 SN1a supernovae z/µ data also indicated that these were well-matched with the TL model.

The interpretation of the RS of atomic spectral lines suffers from the fact that none of the proposed systems (the expanding space paradigm or the TL mechanism) can be confirmed experimentally, meaning that confidence in each hypothesis should be estimated based on its ability to explain the observational data. One important issue in cosmology is therefore to explain which of the two models fits the observed data better, i.e., whether the HD follows the linear (expanding universe) or the exponential TL relation. In the high RS range, it should be more feasible to check more precisely whether the HD follows a linear or exponential slope.

Very exact z/μ data for SN1a supernovae, however, are accessible only for a limited range of distances. At RS > ~ 1.3, the optical light emitted by a supernova gradually diminishes with distance, making definite estimations difficult. Hence, some attempts have been made to collect and use GRB data for computing HDs in the high RS range, Schäfer

[6, 7]

, Wei

[8]

, Amati

[9]

Using mixed SN1a and GRB or exclusively GRB data, Marosi

[10-12]

observed that the slope of the HD is (or is extremely close to) exponential, which is characteristic of the TL model. In contrast, ongoing investigations by Gupta

[13]

and Shirokov et al.

[14, 15]

have found that although none of the existing studies has given probative affirmation for the ΛCDM model, the conclusion can be drawn that based on the HD test, the TL model can be precluded. This cosmologically significant inconsistency between these two contradictory conclusions requires an amendment.

2. Aims

The HD test represents possibly the most significant proof for identifying the underlying physical nature of the Hubble constant (abbreviated as h^CDM = (km s^-1 Mpc^-1)/100 for ΛCDM and h^TL = (Hz s^-1 Hz^-1)/100 for the TL model), and could provide solid support for the expansion hypothesis, or, in the contrary case, for the legitimacy of the TL model (although this would require modification to the ΛCDM itself).

The aim of the present study was to perform a comparative HD test using cosmology-independent SN1a data and high RS GRB RS/μ data. Since both the ΛCDM and the TL model make precise forecasts about the shape of the HD, it ought to be possible to confirm whether the HD shows a linear

(1)

or exponential relationship

(2)

where t represents the flight time of the photons from the co-moving radial distance d to the observer; for simplicity, we will use t instead of d in the following discussion). This could set significant constraints on these contrasting cosmological models.

We do not plan to examine existing issues related to the ΛCDM and TL cosmology, or to accept or reject either model on the basis of hypothetical contentions or hypotheses. The present study is completely cosmology-independent; it is a mathematically based statistical investigation based on cosmology-independent data without the need to turn to cosmological suspicions, meaning that it is unbiased.

3. Datasets and Methods

3.1. SN1a Supernovae

(a) For the model calculations, the cosmological parameters Ώ_M = 0.295, Ώ_λ = 0.705, w = −1.018 and h₀ = 0.7 were used, based on 374 spectroscopically affirmed, upgraded SN1a supernovae from the most recent joint light-curve analysis (JLA) data index, Betoule et al.

[16]

3.2. Choice of GRB Data

(b) 60 low RS and 78 high RS GRB data samples from the Union1 compilation, collected by Liu and Wei

[17]

. One extreme outlier at ln(z+1) = 1.2095 with t = 17491×10^-14 was excluded from the calculation.

[9]

(d) 134 GRB data samples, Demianski

[18]

A comparison of the goodness of fit indicators for data sets b), c) and d) is shown in Table 1.

Table 1. Descriptive statistics from the considered GRB data sets.

Data set	(b)	(c)	(d)
No. of data points	138	193	134
z range	0.031–8.1	0.03354–8.1	1.48–9.3
Data points z ≥ 5	6	5	5
R²	0.8746	0.7848	0.8241
∑χ² (best fit: obs)	1.9193	5.1282	2.8849
∑χ²/data point	0.0139	0.02657	0.02153
Standard deviation	2.196	2.2256	2.2623

Based on the above quality criteria, we selected 138 calibrated, cosmology-independent GRB data points in the RS range z = 0.0331–8.1 for a detailed analysis.

4. Data Processing

Data were introduced on the usual, strongly attenuated logarithmic z/μ scale, and since the contrast between the measured and the modelled data turned out to be clearer on the linear scale, we also considered the less commonly used but more sensitive linear photon flight time t/(z+1) scale. A conspicuous benefit of the t/(z +1) representation is the direct illustration of the shape of the HD, which can be definitively contrasted with the expectations following from Equations (1) and (2).

4.1. Data Conversion from µ to t(d) and Vice Versa

For data conversion from µ to t we used Equation (3), and for conversion from t to µ we used Equations (4) and (5), as follows:

(3)

(4)

(5)

Conversion of the SN1a µ data to a linear scale was straightforward, as the data were of high precision and Equation (3) could directly be applied for conversion without producing disruptive amplification of measurement errors.

Due to experimental difficulties in determining z/μ data at high RS, these data were overwhelmed by substantial scatter, meaning that they could not be converted to the linear t/(z +1) scale without amplifying the scatter and making the converted data unmanageable. Hence, before data conversion, there was a need to either smooth the data scatter by calculating the line of best fit using a suitable arithmetical function or to multiply the t values by an appropriate damping factor, which in this case was selected as 10-14. For data fitting, a third-order polynomial regression was used.

4.2. Goodness of Fit

The goodness of fit was calculated using the likelihood estimator

(6)

4.3. Calculations of RS/µ Data

For the ΔCDM model, the ICRAR cosmology calculator was used to calculate the theoretical z/µ data. For the TL models, the z/µ data were calculated as follows:

(7)

(see: Sorrell

[2]

; Vigoureux, Vigoureux & Langlois

[19]

, Traunmüller

[5]

4.4. Data Presentation

Excel was used for data fitting, refinement, and presentation.

5. Equivocality of the SN1a Supernovae Hubble Diagram

Since for ΛCDM models the distances in Equation (1) are nonlinear in z (the distances are limited by the maximum value for d, i.e., the radius of the universe), it is usual to express d as

. This leads to a linear relationship for the variables

(8)

which are the usual coordinates for the graphical presentation of the HD.

For TL models, it follows from Equation (2) that

(9)

which is linear with distance, with an intercept on zero.

Figure 1 shows the HD calculated with the parameters of the ΛCDM model, as set down by Betoule et al.

[16]

, in the RS range z = 0.01–1.35 for the log(z)/µ presentation. Figure 2 shows the same data plotted on the ln(z+1)/t scale.

The fit parameters and goodness of fit indicators are presented in Tables 2 and 3.

Download: Download full-size image

Figure 1. log(z)/µ Hubble diagram for the 31 calculated z/µ data points. log(z)/µ Hubble diagram for the 31 calculated z/µ data points.

Download: Download full-size image

Figure 2. ln(z+1)/t Hubble diagram for the 31 calculated z/d data points. ln(z+1)/t Hubble diagram for the 31 calculated z/d data points.

Table 2. Fit parameters on the linear log(z) µ and ln(z+1)/t scales. Fit parameters on the linear log(z) µ and ln(z+1)/t scales. Fit parameters on the linear log(z) µ and ln(z+1)/t scales.

	Parameter 1	Parameter 2	Parameter 3	Parameter 0
log fit	0.1009	0.6274	6.3167	44.111
ln fit	−855.33	1366.6	4397.4	0

Table 3. Goodness of fit indicators the linear log(z) µ and ln(z+1)/t scales. Goodness of fit indicators the linear log(z) µ and ln(z+1)/t scales. Goodness of fit indicators the linear log(z) µ and ln(z+1)/t scales.

Fit coordinates	∑χ²µcalc: µ fit	R²	P test	Chiqu-test	F test
log(z)/µ	2.673×10^-5	1	0.9999985	1	0.9987774
ln(z+1)/t	1.810×10^-6	1	1	1	0.9987774

As illustrated by Figures 1 and 2, both Equation (8) (the expanding universe model) and Equation (9) (the TL model) match the calculated data with very high accuracy. The exceptionally small ∑χ² values on the order of 10^-5–10^-6 offer convincing evidence of the equivocality of the ΛCDM and TL model in the low RS range.

Download: Download full-size image

Figure 3. Linear HDs for the calculated data (dots) and for the log(z)/µ (triangles) and d/ln(z+1) (squares) models.

The corresponding linear t/(z+1) HDs were derived by converting µ to t using Equations (3-5) based on the fit coefficients from Equations (8) and (9). The linear HDs for both the log(z) and the ln(z+1) representations and the linear HD for the calculated data are shown in Figure 3.

The three curves (i.e., the one calculated based on the parameters of the ΛCDM model, and the log(z)/µ and d/ln(z+1) lines) have an exponential slope, are closely congruent, and cannot be told apart by visual examination. The corresponding Hubble constants and variances are shown in Table 4.

Table 4. Hubble constants and variances for the linear t/(z+1) HD. Hubble constants and variances for the linear t/(z+1) HD. Hubble constants and variances for the linear t/(z+1) HD.

Model	Calculated data	ln fit	log fit
h	0.6322	0.6322	0.6319
R²	0.99967	0.99967	0.99948

The Hubble constants are similar to within 0.5%, with values of h^TL = 0.6319 for the logarithmic log(z)/µ fit and 0.6322 for the ln(z+1) fit and calculated data.

Based on model calculations using 35 equidistant data points in the RS range z = 0.03–1.02, the h^TL equivalents for h^CDM= 0.68, 0.70 and 0.73 were determined in a similar way. The results are summarised in Table 5.

Table 5. Equivalent values for h^CDM and h^TL. Equivalent values for h^CDM and h^TL. Equivalent values for h^CDM and h^TL.

h^CDM	h^TL	h^TL/h^CDM
73	65.92	0.9031
70	63.22	0.9031
68	61.41	0.9031

An obvious but frequently overlooked outcome is that, as shown in Table 5, the equivalent Hubble constants h^CDM and h^TL are different, and this has a significant effect on the comparative evaluation of the ΛCDM and TL models in the high RS range. It can be seen from Table 6 that the comparison of the observed high RS GRB data with the competing ΛCDM and TL models using h^CDM = h^TL is imprecise.

Table 6. Comparison of ∑ χ² values for h^CDM= 0.70, h^TL= 0.70 and the Best fit h^TL= 0 66 with the observed data in the RS range 0.031–8.1. Comparison of ∑ χ² values for h^CDM= 0.70, h^TL= 0.70 and the Best fit h^TL= 0 66 with the observed data in the RS range 0.031–8.1. Comparison of ∑ χ² values for h^CDM= 0.70, h^TL= 0.70 and the Best fit h^TL= 0 66 with the observed data in the RS range 0.031–8.1.

Model, calc. µ	h^CDM = 0.70	h^TL = 0.66	h^TL = 0.70
∑ χ² µ_obs/µ_calc	1.9415	1.9397	1.9923

The ∑χ² differences between hCDM = 0.70 and hTL = 0.70 for the observed data show that hTL = 0.70 gives the poorest fit, whereas a comparison of hCDM = 0.70 with hTL = 0.66 shows the opposite: the hTL = 0.66 model gives the best fit to the observed data. The use of hTL = hCDM instead of the best fit hTL for comparison inevitably leads to the wrong conclusion, that the TL model does not fit the data and can therefore be rejected. The results presented here show that for a proper comparison of ∑χ² for TL models, the correct approach is a Hubble constant close to the expectation value of hTL, as shown in Table 5, or, depending on data quality (influence of scatter and/or outliers on χ²), the best-fit value of hTL.

6. Hubble Diagram for High RS GRBs

6.1. log(z)/µ Hubble Diagram

The log(z)/µ Hubble diagram is depicted in Figure 4.

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Figure 4. Log(z)/µ Hubble diagram of the observed GRB data. Log(z)/µ Hubble diagram of the observed GRB data.

As the data points for high RS show pronounced scatter, the variance of the fit reaches only R² = 0.8746, and cannot be improved by any other reasonable mathematical function. The fit coefficients are shown in Table 7.

Table 7. Fit coefficients for the log(z)/µ Hubble diagram. Fit coefficients for the log(z)/µ Hubble diagram. Fit coefficients for the log(z)/µ Hubble diagram.

Parameter 1	Parameter 2	Parameter 3	Parameter 0	R²
0.133	0.3156	5.8286	44.0533	0.8746

Figure 5 shows the linear t/(z+1) HDs inferred from the best fit coefficients of the observed data (squares) together with the corresponding exponential h^TL = 0.66 (dots) and the HD for h^CDM = 0.70 (triangles).

h^TL = 0.66 (dots).

The GRB HD exhibits some irregular shape between h^TL = 0.66 and h^CDM = 0.7 with

, and

(µfit, obs stands for calculated magnitudes inferred from the polynomial best-fit function, µTl calc. and µCDM calc. were calculated from h^TL = 0.66 for the TL and from Ώ_M= 0.287, w = -1 and h^CDM = 0.7 for the ΔCDM model, respectively.)

The result favours the TL model, but as can be seen from Figure 5, the deviation from the ideal exponential shape is too large to draw safe conclusions. A profile examination shows systematic deviations, especially at RS ≥ ~ 3–4, where data points are visible above the exponential line.

In summary, the ΔCDM model shows a poorer fit to the HD calculated on the basis of observed data, which suggests a somewhat better but still not correct portrayal of the TL model. No safe conclusion in favour of or against either of the competing models can be drawn from this result.

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Figure 5. h^CDM = 0.7 (triangles), best fit of the observed data (squares). h^CDM = 0.7 (triangles), best fit of the observed data (squares).

6.2. ln(z+1)/t Hubble Diagram

The linear ln(z+1)/t Hubble diagram is shown in Figure 6.

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Figure 6. Linear HD on the t/(z+1) scale of the observed GRB data. Linear HD on the t/(z+1) scale of the observed GRB data.

Despite the extensive scatter in the observed photon flight times even at values of z ≥ ~ 1.4, the ln(z+1)/t diagram is linear. Considering the quality of the data, it shows an astonishingly good variance of R² = 0.8447 that could only be worsened by fitting the observed data with higher-order polynomials. From Figure 6, the equation that describes the photon flight time/z relationship on the t×10^-14 scale that goes into the linear t/(z+1) diagram is

(10)

Figure 7 shows the corresponding t/ln(z+1) HD.

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Figure 7. t/ln(z+1) HD for the observed GRB data. t/ln(z+1) HD for the observed GRB data.

The linear HD has a perfect exponential slope, with h^TL = 0.63 in exceptionally good agreement with the expected value of h^TL = 0.632 obtained from model calculations.

7. Discussion

The results of the ln(z+1)/t-test show that both the low RS SN1a data and the high RS GRB HDs provide an adequately good exponential fit to the observed z/μ data, which is characteristic of TL cosmology. This finding, in turn, implies a static universe. This result is in clear conflict with the predictions of the currently accepted expanding ΛCDM model, which is incompatible with an exponential slope of the HD in the high RS range. Since expansion cannot be measured experimentally, various tests based on observational data have been proposed to provide evidence for the expansion hypothesis; Sandage et al.

[20]

, Sandage, Perlmutter

[21]

, Sandage, Lubin

[22]

, Hubble, Tolman

[23]

, Alcock, Paczyński

[24]

: (i) the Tolman surface brightness test, (ii) the time dilation test, (iii) the cosmic microwave background temperature as a function of the RS test, (iv) the apparent magnitude versus distance test, (v) the angular size versus the RS test and, (vi) the Alcock-Paczynski test have been suggested as possible observational evidence for the expanding space hypothesis. The results of these tests indicate that expansion as predicted by the ɅCDM model with h = 0.7 can be excluded. Static and slowly expanding universe (SEU) models (La Violette, personal communication) fit the observations more accurately, Lopez-Corredoira

[25, 26]

, Cawford

[27]

, LaViolette

[28]

, Lerner

[29]

. Presently, concordance cosmology cannot give convincing explanation to these conflicting results. Uncertainties about the true physical origin of the cosmic redshift, due to expansion or energy loss according to the TL theory, require careful re-evaluation.

8. Uncertainties and Recent Developments

The problem with the Hubble constant is that redshift from local measurements (calculated from the redshift of spectral lines emitted by distant galaxies) and redshift from global measurements (calculated from the CMB power spectrum) lead to different results: H₀(local) = 72-73 km s^-1 Mpc^-1 as compared to H₀(global) = 67.8 km s^-1 Mpc^-1. The significant difference between the local and global measurements is taken so seriously that the need for new physics beyond the current standard model has been discussed in order to explain this discrepancy. Attempts to bring together these two values have been unsuccessful.

A further problem concerns the age of the universe. Recently, the JWST has discovered galaxies appearing older than the universe itself, Gupta

[30]

. Both problems are tightly bound not only to the value but also to the physical nature of the Hubble constant.

Since it cannot be excluded that doe to systematic errors in distance (D) calculations, for example, the magnitude/redshift relation that is essential for the construction of the HD, may be subject to unidentified systematic errors, it is important to have different methods which may not be subject to the same sources of errors. Various fundamentally different methods have been employed determine the accurate value of the Hubble constant such as estimating the Hubble constant with gravitational waves

[31, 32]

and the four - parameter χ²-Test

[33, 34]

. However, these methods have not yet been systematically tested and quantitative comparison with results obtained by other methods is lacking.

9. Conclusions

The most significant conclusion of the HD test introduced in this analysis is that within the low RS range of z = 0.01–1.3, the HD is equivocal and permits no distinction between the ΛCDM and TL models. The HD can be equally well described by the parameters of the ΛCDM model as by the exponential function

In the high RS range up to z = 8.1, the observed z/µ data conflict with the ΛCDM model, and exhibits an exponential slope. This result contradicts many established facts and theories about the universe. Such a significant discrepancy regarding one of the most important cosmological parameters, however, requires further clarification.

Abbreviations

H₀	70 km Mpc^-1 s^-1
h	H₀/100 km Mpc^-1 s^-1 = 0.7
HD	Hubble Diagram
RS	Redshift
GRB	Gamma Ray Burst

Author Contributions

Laszlo Arpad Marosi is the sole author. The author read and approved the final manuscript.

Funding

No funding was acquired for this research.

Data Availability Statement

The author confirms that the data supporting the findings of this study are available within the article and the reference list.

Conflicts of Interest

The author declares no conflict of interest.

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Marosi, L. A. (2025). Hubble Diagram Test of SN1a Supernovae and High Redshift Gamma Ray Bursts. American Journal of Astronomy and Astrophysics, 12(3), 126-134. https://doi.org/10.11648/j.ajaa.20251203.17

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Marosi, L. A. Hubble Diagram Test of SN1a Supernovae and High Redshift Gamma Ray Bursts. Am. J. Astron. Astrophys. 2025, 12(3), 126-134. doi: 10.11648/j.ajaa.20251203.17

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Marosi LA. Hubble Diagram Test of SN1a Supernovae and High Redshift Gamma Ray Bursts. Am J Astron Astrophys. 2025;12(3):126-134. doi: 10.11648/j.ajaa.20251203.17

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@article{10.11648/j.ajaa.20251203.17,
  author = {Laszlo Arpad Marosi},
  title = {Hubble Diagram Test of SN1a Supernovae and High Redshift Gamma Ray Bursts
},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {12},
  number = {3},
  pages = {126-134},
  doi = {10.11648/j.ajaa.20251203.17},
  url = {https://doi.org/10.11648/j.ajaa.20251203.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20251203.17},
  abstract = {Hubble diagrams are examined for SN1a supernovae in the redshift range z = 0.01–1.3 and for gamma ray bursts in the range z = 0.034–8.1. It is shown that in the low redshift range, the Hubble diagram shows an innate equivocality between the ΛCDM and the tired light model. This means that the strong agreement between the z/µ data, calculated with the parameters of the ΛCDM model, and the experimentally measured z/µ values cannot be considered as definite evidence for the expansion hypothesis. The exponential function z+1 = eh(TL) × t(d) which is characteristic of the tired light redshift mechanism, fits the data with similarly high accuracy. Hence, on the premise of low redshift data, a decision for or against either model is completely arbitrary. We expect that in the high RS range it should be possible to check more precisely whether the HD follows the linear H0D/c or the exponential relation, an effect that is not perceptible in the z< 1 region. Unfortunately, SN1a supernovae data are accessible only to a limited range of distances. This constraints on the data motivated several attempts to obtain cosmological parameters from gamma ray bursts observations. GRBs are the most brilliant sources in the universe. Tey are acquired up to RSs of ~8 and higher, and endeavours are made to use GRB data to calculate HD. In this study a total of 138 calibrated, cosmology independent GRB z/μ data points collected by Liu and Wei from the 557 Union2 compilations were used as the starting data set. It is shown that the Hubble diagram for high redshift gamma ray bursts shows poor agreement with the ΛCDM model, but concurs with the exponential energy decay following from the tired light redshift hypothesis.
},
 year = {2025}
}

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TY - JOUR
T1 - Hubble Diagram Test of SN1a Supernovae and High Redshift Gamma Ray Bursts

AU - Laszlo Arpad Marosi
Y1 - 2025/09/11
PY - 2025
N1 - https://doi.org/10.11648/j.ajaa.20251203.17
DO - 10.11648/j.ajaa.20251203.17
T2 - American Journal of Astronomy and Astrophysics
JF - American Journal of Astronomy and Astrophysics
JO - American Journal of Astronomy and Astrophysics
SP - 126
EP - 134
PB - Science Publishing Group
SN - 2376-4686
UR - https://doi.org/10.11648/j.ajaa.20251203.17
AB - Hubble diagrams are examined for SN1a supernovae in the redshift range z = 0.01–1.3 and for gamma ray bursts in the range z = 0.034–8.1. It is shown that in the low redshift range, the Hubble diagram shows an innate equivocality between the ΛCDM and the tired light model. This means that the strong agreement between the z/µ data, calculated with the parameters of the ΛCDM model, and the experimentally measured z/µ values cannot be considered as definite evidence for the expansion hypothesis. The exponential function z+1 = eh(TL) × t(d) which is characteristic of the tired light redshift mechanism, fits the data with similarly high accuracy. Hence, on the premise of low redshift data, a decision for or against either model is completely arbitrary. We expect that in the high RS range it should be possible to check more precisely whether the HD follows the linear H0D/c or the exponential relation, an effect that is not perceptible in the z< 1 region. Unfortunately, SN1a supernovae data are accessible only to a limited range of distances. This constraints on the data motivated several attempts to obtain cosmological parameters from gamma ray bursts observations. GRBs are the most brilliant sources in the universe. Tey are acquired up to RSs of ~8 and higher, and endeavours are made to use GRB data to calculate HD. In this study a total of 138 calibrated, cosmology independent GRB z/μ data points collected by Liu and Wei from the 557 Union2 compilations were used as the starting data set. It is shown that the Hubble diagram for high redshift gamma ray bursts shows poor agreement with the ΛCDM model, but concurs with the exponential energy decay following from the tired light redshift hypothesis.

VL - 12
IS - 3
ER -

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Laszlo Arpad Marosi

Independent Scholar, Ludwigshafen am Rhein, Germany

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http://orcid.org/0000-0002-6935-2587

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Figure 1

Figure 1. log(z)/µ Hubble diagram for the 31 calculated z/µ data points.
Figure 2

Figure 2. ln(z+1)/t Hubble diagram for the 31 calculated z/d data points.
Figure 3

Figure 3. Linear HDs for the calculated data (dots) and for the log(z)/µ (triangles) and d/ln(z+1) (squares) models.
Figure 4

Figure 4. Log(z)/µ Hubble diagram of the observed GRB data.
Figure 5

Figure 5. h^CDM = 0.7 (triangles), best fit of the observed data (squares).
Figure 6

Figure 6. Linear HD on the t/(z+1) scale of the observed GRB data.
Figure 7

Figure 7. t/ln(z+1) HD for the observed GRB data.

Table 1

Table 1. Descriptive statistics from the considered GRB data sets.
Table 2

Table 2. Fit parameters on the linear log(z) µ and ln(z+1)/t scales. Fit parameters on the linear log(z) µ and ln(z+1)/t scales.
Table 3

Table 3. Goodness of fit indicators the linear log(z) µ and ln(z+1)/t scales. Goodness of fit indicators the linear log(z) µ and ln(z+1)/t scales.
Table 4

Table 4. Hubble constants and variances for the linear t/(z+1) HD. Hubble constants and variances for the linear t/(z+1) HD.
Table 5

Table 5. Equivalent values for h^CDM and h^TL. Equivalent values for h^CDM and h^TL.
Table 6

Table 6. Comparison of ∑ χ² values for h^CDM= 0.70, h^TL= 0.70 and the Best fit h^TL= 0 66 with the observed data in the RS range 0.031–8.1. Comparison of ∑ χ² values for h^CDM= 0.70, h^TL= 0.70 and the Best fit h^TL= 0 66 with the observed data in the RS range 0.031–8.1.
Table 7

Table 7. Fit coefficients for the log(z)/µ Hubble diagram. Fit coefficients for the log(z)/µ Hubble diagram.

Plain Text BibTeX RIS

APA Style

Marosi, L. A. (2025). Hubble Diagram Test of SN1a Supernovae and High Redshift Gamma Ray Bursts. American Journal of Astronomy and Astrophysics, 12(3), 126-134. https://doi.org/10.11648/j.ajaa.20251203.17

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ACS Style

Marosi, L. A. Hubble Diagram Test of SN1a Supernovae and High Redshift Gamma Ray Bursts. Am. J. Astron. Astrophys. 2025, 12(3), 126-134. doi: 10.11648/j.ajaa.20251203.17

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AMA Style

Marosi LA. Hubble Diagram Test of SN1a Supernovae and High Redshift Gamma Ray Bursts. Am J Astron Astrophys. 2025;12(3):126-134. doi: 10.11648/j.ajaa.20251203.17

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@article{10.11648/j.ajaa.20251203.17,
  author = {Laszlo Arpad Marosi},
  title = {Hubble Diagram Test of SN1a Supernovae and High Redshift Gamma Ray Bursts
},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {12},
  number = {3},
  pages = {126-134},
  doi = {10.11648/j.ajaa.20251203.17},
  url = {https://doi.org/10.11648/j.ajaa.20251203.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20251203.17},
  abstract = {Hubble diagrams are examined for SN1a supernovae in the redshift range z = 0.01–1.3 and for gamma ray bursts in the range z = 0.034–8.1. It is shown that in the low redshift range, the Hubble diagram shows an innate equivocality between the ΛCDM and the tired light model. This means that the strong agreement between the z/µ data, calculated with the parameters of the ΛCDM model, and the experimentally measured z/µ values cannot be considered as definite evidence for the expansion hypothesis. The exponential function z+1 = eh(TL) × t(d) which is characteristic of the tired light redshift mechanism, fits the data with similarly high accuracy. Hence, on the premise of low redshift data, a decision for or against either model is completely arbitrary. We expect that in the high RS range it should be possible to check more precisely whether the HD follows the linear H0D/c or the exponential relation, an effect that is not perceptible in the z< 1 region. Unfortunately, SN1a supernovae data are accessible only to a limited range of distances. This constraints on the data motivated several attempts to obtain cosmological parameters from gamma ray bursts observations. GRBs are the most brilliant sources in the universe. Tey are acquired up to RSs of ~8 and higher, and endeavours are made to use GRB data to calculate HD. In this study a total of 138 calibrated, cosmology independent GRB z/μ data points collected by Liu and Wei from the 557 Union2 compilations were used as the starting data set. It is shown that the Hubble diagram for high redshift gamma ray bursts shows poor agreement with the ΛCDM model, but concurs with the exponential energy decay following from the tired light redshift hypothesis.
},
 year = {2025}
}

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TY - JOUR
T1 - Hubble Diagram Test of SN1a Supernovae and High Redshift Gamma Ray Bursts

VL - 12
IS - 3
ER -

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