Partial Relief of the Hubble Tension and a Natural Self-Interacting Dark Matter Candidate From Staged Symmetry Breaking

The values of the Hubble constant ($\rm{H_0}$) inferred from the cosmic microwave background (CMB) and local measurements via the distance ladder exhibit a $\sim5σ$ tension. In this work we propose that the tension might be partially alleviated if a subcomponent of the dark matter undergoes decays triggered by spontaneous symmetry breaking in the dark sector, so that the equation of state parameter of the subcomponent shifts from $w \approx 0$ at early times to $w \approx -1/3$ at late times. We provide an effective field theory whose structure is partially motivated by the desire for a plausible UV completion. We find that such a construction naturally produces a possible self-interacting dark matter candidate with a velocity-dependent scattering cross section as a by-product of gauge invariance. This is relevant for addressing tensions between the predictions of $Λ$CDM and observations of small-scale structure, such as the core-cusp problem.

💡 Research Summary

The paper addresses the persistent ∼5σ discrepancy between early‑time (CMB) and late‑time (distance‑ladder) measurements of the Hubble constant H₀. Rather than invoking early dark energy or modifications of gravity, the authors propose a microphysical mechanism in which a sub‑component of dark matter undergoes a staged decay triggered by two successive spontaneous symmetry breakings in a dark sector.

The model contains a complex scalar A (the “cold” dark‑matter component with equation‑of‑state w≈0), a real scalar B (the decay product with w=−1/3), and two dark Higgs fields H₁ and H₂. The dark sector is endowed with a U(1)₁×U(1)₂ gauge symmetry, with gauge bosons αμ and βμ. The Lagrangian (Eq. 3) includes kinetic terms, mass terms, and interaction terms κ|B| H₁†H₁ and g_AB A B² H₂†.

At early times (high redshift) H₁ acquires a vacuum expectation value, breaking U(1)₁. The gauge boson αμ becomes massive and the scalar h₁ (the radial mode of H₁) appears. This generates a coupling g_{h1} αμ α^μ h₁, which later provides a self‑interaction channel for αμ.

At a later epoch (z≈1–2) H₂ obtains a VEV, breaking U(1)₂. The term g_AB A B² becomes active, allowing the decay A→2B with rate Γ_A. The decay switches the equation‑of‑state of the sub‑component from w=0 to w=−1/3, altering the background expansion.

The authors solve the coupled continuity equations for ρ_A, ρ_B, and the Friedmann equation from recombination (z≈1090) to today, using a step function Θ(t−t_break) to model the sudden onset of decay. Free parameters are the initial fraction f_A≡ρ_A/ρ_DM at recombination (0–0.25), the break redshift z_break (0–20), and the decay rate Γ_A (10⁻¹⁸–10⁻¹⁵ s⁻¹). They fit these to a compilation of H(z) measurements (Refs.