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

TL;DR

The paper tackles the Hubble tension between CMB-based and local $H_0$ measurements by proposing a dark-sector mechanism in which a subcomponent of dark matter decays after staged symmetry breaking, driving a late-time EOS shift from $w_A \approx 0$ to $w_B \approx -1/3$ and partially relieving the tension. The model is built as a gauge-invariant two-U(1) theory with fields $A$, $B$, and dark Higgses $H_1$, $H_2$, producing a SIDM candidate via a scalar mediator $h_1$ with velocity-dependent interactions. The authors solve the cosmic energy-density evolution, fit to $H(z)$ data using genetic and grid-based optimization, and identify best-fit parameters around $f_A\approx 0.25$, $z_{BREAK}\approx 1.5$, and $\Gamma_A\approx 8\times10^{-16}\ \mathrm{s}^{-1}$, while also computing a tree-level $\sigma_T$ that decreases with velocity to address small-scale structure. The framework yields a natural SIDM by-product and a potentially testable impact on late-time cosmology and structure, inviting further investigation into ISW/CMB effects, S8 tension, and UV completion details.

Abstract

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.

Figures (6)

• Figure 1: We provide Feynman diagrams for tree-level $\alpha\alpha \to \alpha\alpha$ scattering via a scalar mediator $h_1$. The $t$-channel diagram is on the left and the $u$-channel diagram is on the right.
• Figure 2: We show the best-fit H(z) found using a genetic algorithm (dotted) or grid search + Powell's method (dashed) to fit parameters to measured H(z), shown as black points.
• Figure 3: We show the fractional change in H(z) with our cascade, as compared to $\Lambda$CDM. We use the best-fit parameters found using a genetic algorithm (dotted) or grid search + Powell's method (solid) to fit to measured H(z).
• Figure 4: We plot the tree-level momentum-transfer cross section for the scattering process $\alpha \alpha \to \alpha \alpha$ with $m_\alpha$ = 1 GeV and $m_{h_1} = 1$ MeV. One can see that this decreases with increasing relative velocity, potentially enabling the SIDM to evade constraints from galaxy clusters while still producing cored density profiles in galaxies.
• Figure 5: We plot the tree-level differential cross section for the scattering process $\alpha \alpha \to \alpha \alpha$ with $m_\alpha$ = 1 GeV, $m_{h_1} = 1$ MeV, and a relative velocity of 200 km/sec. This velocity is relevant for the Milky Way scale.