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We update cosmological constraints on two decaying dark matter models inlight of BOSS-DR12 data analyzed under the Effective Field Theory ofLarge-Scale Structures (EFTofLSS) formalism, together with Planck, Pantheon andother BOSS measurements of the baryonic acoustic oscillation (BAO). In thefirst model, a fraction $f_{\rm dcdm}$ of cold dark matter (CDM) decays intodark radiation (DR) with a lifetime $\tau$. In the second model (recentlysuggested as a potential resolution to the $S_8$ tension), all the CDM decayswith a lifetime $\tau$ into DR and a massive warm dark matter (WDM) particle,with a fraction $\varepsilon$ of the CDM rest mass energy transferred to theDR. Using numerical codes from the recent literature, we perform the firstcalculation of the mildly non-linear (matter and galaxy) power spectra with theEFTofLSS for these two models. In the case of DR products, we obtain theconstraints $f_{\rm dcdm}\lesssim0.022$ (95\% C.L.) for lifetimes shorter thanthe age of the universe, and $\tau/f_{\rm dcdm} \gtrsim 250$ Gyr in thelong-lived regime assuming $f_{\rm dcdm}\to1$. We show that Planck datacontributes the most to these constraints, with EFTofBOSS providing a marginalimprovement over conventional BAO and redshift space distortions ($f\sigma_8$)data. In the case of DR and WDM decay products, we find that EFTofBOSS datasignificantly improves the constraints at 68\% C.L. on the CDM lifetime with a$S_8$ prior from KiDS-1000. We show that, in order to fit EFTofBOSS data whilelowering $S_8$ to match KiDS-1000, the best-fit model has a longer lifetime$\tau = 120$ Gyr, with a larger kick velocity $v_{\rm kick}/c \simeq\varepsilon \simeq 1.2\%$, than that without EFTofBOSS ($\tau = 43$ Gyr,$\varepsilon =0.6\%$). We anticipate that future surveys will provide exquisiteconstraints on such models.

Constraining decaying dark matter with BOSS data and the effective field theory of large-scale structures