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

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.