Abstract
In this work we derive constraints on interacting dark matter-dark radiation
models from a full-shape analysis of BOSS-DR12 galaxy clustering data, combined
with Planck legacy cosmic microwave background (CMB) and baryon acoustic
oscillation (BAO) measurements. We consider a set of models parameterized
within the effective theory of structure formation (ETHOS), quantifying the
lifting of the $S_8$ tension in view of KiDS weak-lensing results. The most
favorable scenarios point to a fraction $f10-100\%$ of interacting dark
matter as well as a dark radiation temperature that is smaller by a factor
$\xi0.1-0.15$ compared to the CMB, leading to a reduction of the tension
to the $1\sigma$ level. The temperature dependence of the interaction rate
favored by relaxing the $S_8$ tension is realized for a weakly coupled unbroken
non-Abelian $SU(N)$ gauge interaction in the dark sector. To map our results
onto this $SU(N)$ model, we compute higher-order corrections due to Debye
screening. We find a lower bound $\alpha_dg_d^2/(4\pi)10^-8
(10^-9)$ for dark matter mass $1000 (1)$ GeV for relaxing the $S_8$ tension,
consistent with upper bounds from galaxy ellipticities and compatible with
self-interactions relevant for small-scale structure formation.
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