Title: Is there still room for low-z solutions to the Hubble tension?

Abstract: The  ∼5\sigma mismatch between the value of the Hubble parameter measured by SH0ES and the one inferred from the inverse distance ladder (IDL) constitutes the biggest tension afflicting the standard model of cosmology, which could be pointing to the need of physics beyond LCDM. In this talk I will review the background history required to solve the H0 tension if we consider standard prerecombination physics, paying special attention to the role played by the data on baryon acoustic oscillations (BAO) employed to build the IDL.  I will show that the anisotropic BAO data favor an ultra-late-time (phantom-like) enhancement of H(z) at z<0.2, accompanied by a transition in the absolute magnitude of supernovae of Type Ia M(z) in the same redshift range. The effective dark energy (DE) density must be smaller than in the standard model at higher redshifts. Instead, when angular BAO data (claimed to be less subject to model dependencies) is employed in the analysis, the increase of H(z) must start at much higher redshifts, typically in the range z= 0.5-0.8. In this case, M(z) could experience also a transition (although much smoother) and the effective DE density becomes negative at z\sim 2. Both scenarios require a violation of the weak energy condition, but leave an imprint on completely different redshift ranges and might also have a different impact on the perturbed observables. They allow for the effective crossing of the phantom divide. I will put the accent on the utmost importance of the choice of the BAO data set in the study of the possible solutions to the H0 tension.