A Hidden Dark Matter Sector, Dark Radiation, and the CMB

TL;DR

The paper investigates a DM framework in which a weak-scale thermal relic annihilates predominantly into a light hidden sector, producing dark radiation that contributes to the CMB energy density as $\Delta N_\text{eff}$ and modifies both scalar and tensor perturbations. It develops a two-temperature formalism to compute relic abundance and DR effects, derives a robust lower bound on $\Delta N_\text{eff}$, and shows that the DR can be either free-streaming or self-interacting, yielding opposite imprints on the CMB peak structure and tensor damping. A simple Higgs-portal benchmark with a hidden U(1) sector demonstrates compatibility with Planck results and yields signals detectable by future missions such as CMBPol and Stage-IV, while invisible Higgs decays offer a complementary collider probe. The work highlights how upcoming CMB measurements can probe hidden dark sectors and distinguish DR dynamics, providing a path to testing DM scenarios beyond traditional direct/indirect detection approaches.

Abstract

We consider theories where dark matter is composed of a thermal relic of weak scale mass, whose couplings to the Standard Model (SM) are however too small to give rise to the observed abundance. Instead, the abundance is set by annihilation to light hidden sector states that carry no charges under the SM gauge interactions. In such a scenario the constraints from direct and indirect detection, and from collider searches for dark matter, can easily be satisfied. The masses of such light hidden states can be protected by symmetry if they are Nambu-Goldstone bosons, fermions, or gauge bosons. These states can then contribute to the cosmic energy density as dark radiation, leading to observable signals in the cosmic microwave background (CMB). Furthermore, depending on whether or not the light hidden sector states self-interact, the fraction of the total energy density that free-streams is either decreased or increased, leading to characteristic effects on both the scalar and tensor components of the CMB anisotropy that allows these two cases to be distinguished. The magnitude of these signals depends on the number of light degrees of freedom in the hidden sector, and on the temperature at which it kinetically decouples from the SM. We consider a simple model that realizes this scenario, based on a framework in which the SM and hidden sector are initially in thermal equilibrium through the Higgs portal, and show that the resulting signals are compatible with recent Planck results, while large enough to be detected in upcoming experiments such as CMBPol and CMB Stage-IV. Invisible decays of the Higgs into hidden sector states at colliders can offer a complementary probe of this model.

Figures (5)

• Figure 1: $\Delta N_{\text{eff}}$ as a function of the temperature at which the SM and dark sector thermally decouple. Also shown are the 2015 Planck results: the central value (Green dashed line) and the $2 \sigma$ constraint (Orange dashed line).
• Figure 2: Relative change in tensor mode anisotropy compared to the SM case ($N_\text{eff}=3.046$), $R=\left|\dfrac{\chi'(u)}{\chi'_\text{SM}(u)} \right|^2$, for short wavelengths.
• Figure 3: Relative change in tensor mode anisotropy compared to the SM case ($N_\text{eff}=3.046$), $R=\left|\dfrac{\chi'(y_{\rm dec})}{\chi'_\text{SM}(y_{\rm dec})} \right|^2$, for varying $\Delta N_{\rm eff}^{\rm free}$ (shorthand $\Delta N_{\rm FS}$) and $\Delta N_{\rm eff}^{\rm scatt}$ (shorthand $\Delta N_{\rm SC}$), for long wavelengths.
• Figure 4: The kinetic decoupling temperature $T_\text{kd}$ between the SM and hidden sectors as a function of the DM mass $m_\text{DM}$ for three values of $\kappa$: $\kappa_\text{LHC14} = 7 \times 10^{-3}, \kappa_\text{ILC02} = 9.5 \times 10^{-4}$ and $\kappa = 5 \times 10^{-6}$.
• Figure 5: $\Delta N_{\text{eff}}$ and $\Delta \ell$ as a function of $m_{\text{DM}}$. It is assumed that $M_{\hat{Z}} > m_{\text{DM}}$. Three values of $\kappa$ are considered: $\kappa_\text{LHC14}, \kappa_\text{ILC02}$ and $\kappa = 5 \times 10^{-6}$. Also shown are the 2015 Planck results: the central value (Green dashed line) and the $2 \sigma$ constraint (Orange dashed line).