PreprintArticleVersion 2This version is not peer-reviewed
Closed Form Solution to the Hubble Tension Based on Rh = ct Cosmology for Generalized Cosmological Redshift Scaling of the Form: z = (Rh/Rt)x −1 Tested against the full Distance Ladder of Observed SN Ia Redshift
Version 1
: Received: 22 September 2024 / Approved: 23 September 2024 / Online: 23 September 2024 (12:25:43 CEST)
Version 2
: Received: 28 September 2024 / Approved: 30 September 2024 / Online: 30 September 2024 (13:48:08 CEST)
How to cite:
Haug, E. Closed Form Solution to the Hubble Tension Based on Rh = ct Cosmology for Generalized Cosmological Redshift Scaling of the Form: z = (Rh/Rt)x −1 Tested against the full Distance Ladder of Observed SN Ia Redshift. Preprints2024, 2024091697. https://doi.org/10.20944/preprints202409.1697.v2
Haug, E. Closed Form Solution to the Hubble Tension Based on Rh = ct Cosmology for Generalized Cosmological Redshift Scaling of the Form: z = (Rh/Rt)x −1 Tested against the full Distance Ladder of Observed SN Ia Redshift. Preprints 2024, 2024091697. https://doi.org/10.20944/preprints202409.1697.v2
Haug, E. Closed Form Solution to the Hubble Tension Based on Rh = ct Cosmology for Generalized Cosmological Redshift Scaling of the Form: z = (Rh/Rt)x −1 Tested against the full Distance Ladder of Observed SN Ia Redshift. Preprints2024, 2024091697. https://doi.org/10.20944/preprints202409.1697.v2
APA Style
Haug, E. (2024). Closed Form Solution to the Hubble Tension Based on R<sub>h </sub>= ct Cosmology for Generalized Cosmological Redshift Scaling of the Form: z = (R<sub>h</sub>/R<sub>t</sub>)x −1 Tested against the full Distance Ladder of Observed SN Ia Redshift. Preprints. https://doi.org/10.20944/preprints202409.1697.v2
Chicago/Turabian Style
Haug, E. 2024 "Closed Form Solution to the Hubble Tension Based on R<sub>h </sub>= ct Cosmology for Generalized Cosmological Redshift Scaling of the Form: z = (R<sub>h</sub>/R<sub>t</sub>)x −1 Tested against the full Distance Ladder of Observed SN Ia Redshift" Preprints. https://doi.org/10.20944/preprints202409.1697.v2
Abstract
Haug and Tatum [1, 2] have recently outlined a possible path to solving the Hubbletension within Rh = ct cosmology models using a trial-and-error algorithm for redshift scaling, 1 specifically z = (R_h/R_t) − 1 and z = (R_h/R_t)^{1/2}-1 . Their algorithm demonstrates that one canstart with the measured CMB temperature and a rough estimate of H_0. Based on this approach, they nearly perfectly match the entire distance ladder of observed supernovae by identifying a single value for H_0. However, their solution is based on a simple numerical search procedure, which, although it can be completed in a fraction of a second on a standard computer, is not a formal mathematical proof for resolving the Hubble tension.Here, we will demonstrate that the trial-and-error numerical method is not necessary and that the Hubble tension can be resolved using the same Haug and Tatum type R_h = ct model through a closed-form mathematical solution. Furthermore, we will prove that this solution is valid for a much more general case of any cosmological redshift scaling consistent with: z = (R)h/R)t)^x − 1. Haug and Tatum have only considered the most common assumptions of x = 1 and x = 1/2 .Our solution involves simply solving an equation to determine the correct value of H0. This is possible because an exact mathematical relation between H_0 and the CMB temperature has recently been established, in combination with the linearity in an R_h = ct model. We also demonstrate that a thermodynamic form of the Friedmann equation is consistent with a wide range of redshift scalings, namely: z = (R_h/R_t)^x − 1.
Keywords
Hubble tension close dorm; Hubble constant; Cosmological redshift; z; CMB temperatur
Subject
Physical Sciences, Astronomy and Astrophysics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
