Hot New Early Dark Energy Bridging Cosmic Gaps: Supercooled Phase Transition Reconciles (stepped) Dark Radiation Solutions to the Hubble Tension with BBN

We propose a simple model that can alleviate the H 0 tension while remaining consistent with big bang nucleosynthesis (BBN). It is based on a dark sector described by a standard Lagrangian featuring a SU(N) ( N ) gauge symmetry with N >= 3 and a massive scalar field with a quartic coupling. The scalar acts as a dark Higgs leading to spontaneous symmetry breaking SU(N) ( N ) -> SU(N ( N - 1 ) via a first-order phase transition a` la Coleman-Weinberg. This setup naturally realizes previously proposed scenarios featuring strongly interacting dark radiation (SIDR) with a mass threshold within hot new early dark energy. For a wide range of reasonable model parameters, the phase transition occurs between the BBN and recombination epochs and releases a sufficient amount of latent heat such that the model easily respects bounds on extra radiation during BBN while featuring a sufficient SIDR density around recombination for increasing the value of H 0 inferred from the cosmic microwave background. Our model can be summarized as a natural mechanism providing two successive increases in the effective number of relativistic degrees of freedom after BBN but before recombination Delta N BBN -> Delta N NEDE -> Delta N IR alleviating the Hubble tension. The first step is related to the phase transition, and the second is related to the dark Higgs becoming nonrelativistic. This setup predicts further signatures, including a stochastic gravitational wave background and features in the matter power spectrum that can be searched for with future pulsar timing and Lyman-alpha forest measurements.