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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
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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:
Subject: Physical Sciences - Astronomy and Astrophysics
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
Submitted:
04 November 2024
Posted:
05 November 2024
Withdrawn:
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This version is not peer-reviewed
Submitted:
04 November 2024
Posted:
05 November 2024
Withdrawn:
Invalid date
You are already at the latest version
Alerts
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:
Subject: Physical Sciences - Astronomy and Astrophysics
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
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