DESI-Like Hubble Expansion From Staged Symmetry Breaking: Constraints on Renormalizable Models

Abstract

The Dark Energy Spectroscopic Instrument (DESI) second data release shows a moderate preference for dark energy with a time-varying equation of state parameter, suggesting that the standard $\Lambda$CDM model may need to be revised. In particular, DESI favors dark energy whose equation of state parameter can drop below $-1$, violating the null energy condition. Chen and Loeb have recently suggested that this violation may be avoided if a subcomponent of the dark matter possesses a time-dependent equation of state. In this work, we explore the space of possible models, in an effort to find a natural, renormalizable realization. We find that once one requires the model to be renormalizable, a construction that generates the desired expansion history is fairly broadly obstructed. While we are unable to produce a fully natural, renormalizable realization of their ideas, this work is valuable for constraining directions one might pursue for viable theoretical explanations of the DESI results. Our framework is also interesting for incorporating features that may be of interest for model building elsewhere, as our decay cascades enable decays that switch on at particular redshifts while also naturally incorporating a self-interacting dark matter candidate with a velocity-dependent cross section as a consequence of gauge invariance. The second feature is relevant for addressing tensions between $\Lambda$CDM and observations of small-scale structure, particularly the diversity of galactic rotation curves.