Symmetry-Protected Momentum Exchange between Dark Matter and Dark Energy

Abstract

We present a particle physics motivated realization of interacting dark energy in which a radiatively stable dark energy sector couples to weakly interacting massive particle dark matter through pure momentum exchange. The dark energy field arises as a pseudo-Nambu-Goldstone Boson from a complex scalar singlet charged under a softly broken global $U(1)_S$, while dark matter is identified with an inert scalar doublet stabilized by a discrete $Z_4$ symmetry. This symmetry structure allows renormalizable dark matter-dark energy portal operators; however, requiring the dark energy field to emerge as a radiatively stable pseudo-Nambu-Goldstone Boson necessitates their absence, leaving derivative interactions as the leading coupling. As a result, energy transfer between the dark sectors is absent at the background level, while momentum exchange modifies the evolution of cosmological perturbations. We implement the resulting interacting dark energy model self-consistently in the Boltzmann code CLASS and study its impact on the growth of structure. We find that, despite sizeable momentum exchange, the suppression of the clustering amplitude $σ_8$ saturates above the level required to fully resolve current low-redshift tensions. Our results demonstrate that symmetry-protected, momentum-exchange-only dark sector interactions possess an intrinsic limit on structure suppression, providing a theoretically controlled benchmark for interacting dark energy scenarios.

Figures (3)

• Figure 1: Dark matter relic density $\Omega_{\rm DM}h^2$ as a function of the Higgs portal coupling $\lambda_L = \lambda_3 + \lambda_4 + \lambda_5$ for various mass splittings $\delta$, with $m_{H_2^0} = m_{H_2^\pm} = 550$ GeV. The horizontal bands indicate the Planck constraint $\Omega h^2 = 0.1199 \pm 0.0027$. Small splittings ($\delta \lesssim 1$ GeV) allow coannihilation effects to bring the relic density into the observed range.
• Figure 2: Dark matter relic density as a function of the effective coupling $g_{H_1 H_1 h} = 2\lambda_L v$LopezHonorez2007 for $\delta = 1$ GeV and varying $m_{\rm DM} \equiv m_{H_2^0}$. The horizontal bands indicate the Planck constraint. Heavier dark matter particles require larger portal couplings to achieve the observed relic density; the value $m_{\rm DM} \approx 550$ GeV (blue curve) satisfies the Planck bound for natural couplings, consistent with results in the literature Keus2015.
• Figure 3: Clustering amplitude $\sigma_8$ as a function of the normalized drag rate $\Gamma/H$ for the Z$_4$-IDSM with parameters (\ref{['eq:dm_params']}). The horizontal black line shows the CLASS$\Lambda$CDM baseline $\sigma_8^{\Lambda\text{CDM}} = 0.825$. The green (red) shaded region indicates perturbative (non-perturbative) values of the EFT coupling $c_6$. The IDSM prediction saturates at $\sigma_8 \approx 0.795$ for $\Gamma/H \gtrsim 10$.