DESI-Like Hubble Expansion From Staged Symmetry Breaking

TL;DR

The paper addresses DESI’s hints of dynamical dark energy by constructing a natural effective field theory in which a subcomponent of dark matter undergoes a staged symmetry breaking to produce four distinct effective equations of state $w$ (via a decay cascade $\mathrm{A} \to \mathrm{B} \to \mathrm{C} \to \mathrm{D}$). The authors develop a fiducial model with four complex scalars charged under a $U(1)_1\times U(1)_2\times U(1)_3\times U(1)_4$ gauge group, whose sequential symmetry breaking activates decays and a square-root potential term that yields transient $w_C<0$, while generically renormalizable interactions (except one term) ensure theoretical consistency. A by-product of the construction is a self-interacting dark matter candidate with a velocity-dependent cross section mediated by a light scalar; the cross section is computed from full tree-level $t$- and $u$-channel diagrams and shown to decrease with relative velocity, potentially reconciling small-scale structure with cluster constraints. Numerically solving coupled density evolution equations yields an $H(z)$ compatible with DESI trends, and comparisons to a $w_0-w_a$CDM parametrization demonstrate qualitative agreement. The work offers a pathway to connect DESI’s expansion history hints with SIDM phenomenology, while outlining future directions for data fitting, large-scale structure implications, production mechanisms, and possible decoupled quintessence scenarios.

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 $Λ$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 present a realization of that idea which can be regarded as a more natural effective field theory. We show that such a construction not only yields dark matter with a time-varying equation of state parameter, but also naturally produces 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 $Λ$CDM and observations of small-scale structure, particularly the diversity of galactic rotation curves.

Figures (5)

• Figure 1: We show Feynman diagrams for tree-level $\alpha\alpha \to \alpha\alpha$ scattering via a scalar mediator $h$. The $t$-channel diagram is shown on the left and the $u$-channel diagram on the right.
• Figure 2: The fractional change in H(z) with our cascade compared to $\Lambda$CDM (solid). We also include a curve corresponding to dynamical dark energy with $w_0 = -0.83$ and $w_a = -0.62$, which produce behavior similar to that favored by DESI (dashed).
• Figure 3: We plot the tree-level momentum-transfer cross section for the scattering process $\alpha \alpha \to \alpha \alpha$ with $m_\alpha$ = 1 GeV and $m_h = 1$ 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 4: We plot the tree-level differential cross section for the scattering process $\alpha \alpha \to \alpha \alpha$ with $m_\alpha$ = 1 GeV, $m_h = 1$ MeV, and a relative velocity of 200 km/sec. This velocity is relevant for the Milky Way scale.
• Figure 5: We plot the tree-level differential cross section for the scattering process $\alpha \alpha \to \alpha \alpha$ with $m_\alpha$ = 1 GeV, $m_h = 1$ MeV, and a relative velocity of 1000 km/sec. This velocity is relevant for the cluster scale. One can see that this cross section is suppressed as compared to the result for 200 km/sec.