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We present a model describing the dark sector (DS) featured by twointeractions remaining efficient until late times in the matter-dominated eraafter recombination: the interaction among dark radiations (DR), and theinteraction between a small fraction of dark matter and dark radiation. Thedark sector consists of (1) a dominant component cold collisionless DM (DM1),(2) a sub-dominant cold DM (DM2) and (3) a self-interacting DR. When asufficient amount of DR is ensured and a few percent of the total DM density iscontributed by DM2 interacting with DR, this set-up is known to be able toresolve both the Hubble and $\sigma_{8}$ tension. In light of this, we proposea scenario which is logically natural and has an intriguing theoreticalstructure with a hidden unbroken gauge group ${\rm SU}(5)_{\rm X}\otimes {\rmU}(1)_{\rm X}$. Our model of the dark sector does not introduce any new scalarfield, but contains only massless chiral fermions and gauge fields in theultraviolet (UV) regime. As such, it introduces a new scale (DM2 mass, $m_{\rmDM2}$) based on the confinement resulting from the strong dynamics of ${\rmSU}(5)_{\rm X}$. Both DM2-DR and DR-DR interactions are attributed to anidentical long range interaction of ${\rm U}(1)_{\rm X}$. We show that ourmodel can address the cosmological tensions when it is characterized by $g_{\rmX}=\mathcal{O}(10^{-3})-\mathcal{O}(10^{-2})$, $m_{\rmDM2}=\mathcal{O}(1)-\mathcal{O}(100){\rm GeV}$ and $T_{\rm DS}/T_{\rmSM}\simeq0.3-0.4$ where $g_{\rm X}$ is the gauge coupling of ${\rm U}(1)_{\rmX}$ and $T_{\rm DS}$ ($T_{\rm SM}$) is a temperature of the DS (Standard Modelsector). Our model explains candidates of DM2 and DR, and DM1 can be any kindof CDM.

A Model of Interacting Dark Matter and Dark Radiation for $H_{0}$ and $\sigma_{8}$ Tensions