Use of Redshifts as Evidence of Dark Energy

The large-scale dynamics of the universe is generally described in terms of the time-dependent scale factor $a\left(t\right)$. To make contact with observational data, the $a\left(t\right)$ function needs to be related to the observable $z\left(r\right)$ function, redshift versus distance. Model fitting of data has shown that the equation that governs $z\left(r\right)$ needs to contain a constant term, which has been identified as Einstein’s cosmological constant. Here, it is shown that the required constant term is not a cosmological constant but is due to an overlooked geometric difference between proper time t and look-back time $t_{\mathrm{lb}}$ along lines of sight, which fan out isotropically in all directions of the 3D (3-dimensional) space that constitutes the observable universe. The constant term is needed to satisfy the requirement of spatial isotropy in the local limit. Its magnitude is independent of the epoch in which the observer lives and agrees with the value found by model fitting of observational data. Two of the observational consequences of this explanation are examined: an increase in the age of the universe from 13.8 Gyr to 15.4 Gyr, and a resolution of the $H_0$ tension, which restores consistency to cosmological theory.