A flexible parameterization to test early physics solutions to the Hubble tension with future CMB data

One approach to reconciling local measurements of a high expansion rate with observations of acoustic oscillations in the CMB and galaxy clustering (the “Hubble tension”) is to introduce additional contributions to the ΛCDM model that are relevant before recombination. While numerous possibilities exist, none are currently well-motivated or preferred by data. However, future CMB experiments, which will measure acoustic peaks to much smaller scales and resolve polarization signals with higher signal-to-noise ratio over large sky areas, should detect almost any such modification at high significance. We propose a method to capture most relevant possible deviations from ΛCDM due to additional non-interacting components, while remaining sufficiently constraining to enable detection across various scenarios. The phenomenological model uses a fluid model with four parameters governing additional density contributions that peak at different redshifts, and two sound speed parameters. We forecast possible constraints with Simons Observatory, explore parameter degeneracies that arise in ΛCDM, and demonstrate that this method could detect a range of specific models. Which of the new parameters gets excited can give hints about the nature of any new physics, while the generality of the model allows for testing with future data in a way that should not be plagued by a posteriori choices and would reduce publication bias. When testing our model with Planck data, we find good consistency with the ΛCDM model, but the data also allows for a large Hubble parameter, especially if the sound speed of an additional component is not too different from that of radiation. The analysis with Planck data reveals significant volume effects, requiring careful interpretation of results. We demonstrate that Simons Observatory data will mitigate these volume effects, so that any indicated solution to the Hubble tension using our model cannot be mimicked by volume effects alone, given the significance of the tension.