Scaling Transformations and the Origins of Light Relics Constraints from Cosmic Microwave Background Observations

We use here a family of scaling transformations, that scale key rates in the evolution equations, to analytically understand constraints on light relics from cosmic microwave background (CMB) maps, given cosmological models of varying degrees of complexity. We describe the causes of physical effects that are fundamentally important to the constraining power of the data, with a focus on the two that are most novel. We use as a reference model a cosmological model that admits a scaling transformation that increases light relic energy density while avoiding all of these causes. Constraints on light relics in a given model can then be understood as due to the differences between the given model and the reference model, as long as the additional light relics only interact gravitationally with the Standard Model components. This understanding supports the development of cosmological models that can evade light relics constraints from CMB maps.