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We make the case that there can be no low-redshift solution to the $H_0$tension. To robustly answer this question, we use a very flexibleparameterization for the dark energy equation of state such that everycosmological distance still allowed by data exists within this prior volume. Tothen answer whether there exists a satisfactory solution to the $H_0$ tensionwithin this comprehensive parameterization, we constrained the parametric formusing different partitions of the Planck cosmic microwave background,SDSS-IV/eBOSS DR16 baryon acoustic oscillation, and Pantheon supernovadatasets. When constrained by just the cosmic microwave background dataset,there exists a set of equations of state which yields high $H_0$ values, butthese equations of state are ruled out by the combination of the supernova andbaryon acoustic oscillation datasets. In other words, the constraint from thecosmic microwave background, baryon acoustic oscillation, and supernovadatasets together does not allow for high $H_0$ values and converges around anequation of state consistent with a cosmological constant. Thus, since thisvery flexible parameterization does not offer a solution to the $H_0$ tension,there can be no solution to the $H_0$ tension that adds physics at only lowredshifts. This is directly related to the expansion history of the Universeand its geometrical properties and would include models beyond thoseparametrized by $w(z)$.

Ruling Out New Physics at Low Redshift as a solution to the $H_0$ Tension