Solving the Hubble tension at intermediate redshifts with dynamical dark energy

The current expansion rate of the Universe, the Hubble constant $H_0$, is an important cosmological quantity. However, two different ways to measure its value do not agree -- building a low-redshift distance ladder leads to a higher value of $H_0$ than inferring it from high-redshift observations in a $\Lambda$CDM cosmology. Most approaches to solve this tension either act at very low redshift by modifying the local distance ladder, or at high redshift by introducing new physics that changes the normalization of the inverse distance ladder. Here we discuss a way to address the Hubble tension at intermediate redshifts instead. By keeping the low- and high-redshift normalizations unchanged, we find a violation of the distance duality in the redshift range where luminosity and angular diameter distances overlap. We 'solve' this problem by introducing a redshift-dependent systematic effect that brings the luminosity distance into agreement with the angular diameter distance. The resulting expansion history is no longer compatible with $\Lambda$CDM, but this can be fixed with a dynamical dark energy component. In this way, we are able to solve the Hubble tension at intermediate redshifts.