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Recent weak lensing surveys have revealed that the direct measurement of the parameter combination S8≡σ8(Ωm/0.3)0.5S8​≡σ8​(Ωm​/0.3)0.5-- where σ8σ8​ is a measure of the amplitude of matter fluctuations on 8 h−1h−1Mpc scales -- is ∼3σ∼3σ discrepant with the value reconstructed from cosmic microwave background (CMB) data assuming the ΛΛCDM model. In this article, we show that it is possible to resolve the tension if dark matter (DM) decays with a lifetime of Γ−1≃55 GyrsΓ−1≃55 Gyrs into one massless and one massive product, and transfers a fraction ε≃0.7 %ε≃0.7 % of its rest mass energy to the massless component. The velocity-kick received by the massive daughter leads to a suppression of gravitational clustering below its free-streaming length, thereby reducing the σ8σ8​ value as compared to that inferred from the standard ΛΛCDM model, in a similar fashion to massive neutrino and standard warm DM. Contrarily to the latter scenarios, the time-dependence of the power suppression and the free-streaming scale allows the 2-body decaying DM scenario to accommodate CMB, baryon acoustic oscillation, growth factor and un-calibrated supernova Ia data. We briefly discuss implications for DM model building, galactic small-scale structure problems and the recent Xenon-1T excess. Future experiments measuring the growth factor to high accuracy at 0≲z≲10≲z≲1 can further test this scenario.

The Hubble tension can be addressed by modifying the sound horizon ($r_s$) before recombination, triggering interest in $r_s$-free early-universe estimates of the Hubble constant, $H_0$. Constraints on $H_0$ from an $r_s$-free analysis of the full shape BOSS galaxy power spectra within LCDM were recently reported and used to comment on the viability of physics beyond LCDM. Here we demonstrate that $r_s$-free analyses with current data depend on the model and the priors placed on the cosmological parameters, such that LCDM analyses cannot be used as evidence for or against new physics. We find that beyond-LCDM models which introduce additional energy density with significant pressure support, such as early dark energy (EDE) or additional neutrino energy density ($\Delta N_{\rm eff}$), lead to larger values of $H_0$. On the other hand, models which only affect the time of recombination, such as a varying electron mass ($\Delta m_e$), produce $H_0$ constraints similar to LCDM. Using BOSS data, constraints from light element abundances, cosmic microwave background (CMB) lensing, a CMB-based prior on the scalar amplitude ($A_s$), spectral index ($n_s$), and $\Omega_m$ from the Pantheon+ supernovae data set, we find that in LCDM, $H_0=64.9\pm 2.2$ km/s/Mpc; EDE, $H_0=68.7^{+3}_{-3.9}$; $\Delta N_{\rm eff}$, $H_0=68.1^{+2.7}_{-3.8}$; $\Delta m_e$, $H_0=64.7^{+1.9}_{-2.3}$. Using a prior on $\Omega_m$ from uncalibrated BAO and CMB measurements of the projected sound horizon, these values become in LCDM, $H_0=68.8^{+1.8}_{-2.1}$; EDE, $H_0=73.7^{+3.2}_{-3.9}$; $\Delta N_{\rm eff}$, $H_0=72.6^{+2.8}_{-3.7}$; $\Delta m_e$, $H_0=68.8\pm 1.9$. With current data, none of the models are in significant tension with SH0ES, and consistency tests based on comparing $H_0$ posteriors with and without $r_s$ marginalization are inconclusive with respect to the viability of beyond LCDM models.