Improving Constraints on Models Addressing the Hubble Tension with CMB Delensing

The Hubble Tension is a well-known issue in modern cosmology that refers to the apparent disagreement in inferences of the Hubble constant $H_0$ as found through low-redshift observations and those derived from the $\Lambda$CDM model utilizing early universe observations. Several extensions to $\Lambda$CDM have been proposed to address the Hubble Tension that involve new ingredients or dynamics in the early universe. Reversing the effects of gravitational lensing on cosmic microwave background (CMB) maps produces sharper acoustic peaks in power spectra and allows for tighter constraints on cosmological parameters. We investigate the efficacy of CMB delensing for improving the constraints on parameters used in extensions of the $\Lambda$CDM model that are aimed at resolving the Hubble Tension (such as varying fundamental constants, contributions from early dark energy, and self-interacting dark radiation). We use Fisher forecasting to predict the expected constraints with and without this delensing procedure. We demonstrate that CMB delensing improves constraints on $H_0$ by $\sim$ 20% for viable models and significantly improves constraints on parameters across the board in the low-noise regime.