TITLE:
Closed Form Solution to the Hubble Tension Based on R H t =ct Cosmology for Generalized Cosmological Redshift Scaling of the Form: z= ( R H 0 / R H t ) x −1 Tested against the Full Distance Ladder of Observed SN Ia Redshift
AUTHORS:
Espen Gaarder Haug
KEYWORDS:
Hubble Tension Close Dorm, Hubble Constant, Cosmological Redshift, CMB Temperature
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.10,
October
28,
2025
ABSTRACT: Haug and Tatum have recently outlined a possible path to solving the Hubble tension within
R
H
t
=ct
cosmology models using a trial-and-error algorithm for redshift scaling, specifically
z=(
R
H
0
/
R
H
t
)−1
and
z=
(
R
H
0
/
R
H
t
)
1
2
−1
. Their algorithm demonstrates that one can start 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
. This work replaces a previous numerical approach with a formal, 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
0
/
R
H
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
H
0
. 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
t
=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
0
/
R
H
t
)
x
−1
.