Interpreting DESI 2024 BAO: late-time dynamical dark energy or a local effect?

We perform fits to DESI, CMB and supernova data to understand the physical origin of the DESI hint for dynamical dark energy. We find that the linear parametrization of the equation of state w may guide to misleading interpretations, such as the hint for a phantom Universe, which are not preferred by the data. Instead, physical quintessence models fit the data well. Model-independently, present observations prefer deviations from the constant dark energy, w=-1, only at very low redshifts, z < O (0. 1). We find that this result is driven by low-z supernova data. Therefore, either the fundamental properties of our Universe, characterised by the equation of state w and the Hubble parameter H, underwent dramatic changes very recently or, alternatively, we do not fully understand the systematics of our local Universe in a radius of about 300\, h^-1 Mpc.