A changing Hubble constant with distance could be a sign of evolving, ‘phantom’ dark energy
Researchers propose that an apparent change in the measured Hubble constant with redshift — that is, with cosmic distance and time — can be reinterpreted as a sign that dark energy itself is evolving. Working under the common assumption that ordinary matter and dark energy do not directly exchange energy, they show that any effective “running” Hubble constant can be rewritten as a Friedmann equation with an evolving dark energy component that has a definite equation of state.
The authors build a mathematical mapping from a phenomenological, redshift-dependent Hubble function h(z) to a physical dark energy density and its equation-of-state parameter w_DE(z). That mapping is fixed so that, if the Hubble function does not run (h(z)=1) the usual cosmological-constant case with w_DE = −1 is recovered. To test the idea against data, they use the Pantheon compilation of 1,048 Type Ia supernovae, grouped into 40 equally populated redshift bins, and fit simple running functions to the binned Hubble behaviour.
They examine two specific fits. One is a power-law type model in which the running Hubble factor scales exponentially with a parameter (previously fit in other work). The other is an “optimized” form that approaches the constant value at low redshift and departs slightly at higher redshift; for that model the best-fit deviation parameter is reported as −0.0158 ± 0.0059. Both fits reproduce the binned Supernova data better than a model with a single constant Hubble constant, and the two running models are hard to distinguish from each other with this dataset.
When the fitted running Hubble functions are translated into a physical dark energy component, the inferred equation of state lies on the “phantom” side, meaning w_DE < −1. In plain terms, a phantom equation of state implies dark energy density that would grow with time rather than remain constant. The authors emphasize that this conclusion follows directly from their mapping and from the fitted running functions, given the non-interaction assumption between matter and dark energy.