Constraining decaying dark matter with BOSS data and the effective field
  theory of large-scale structures
  We update cosmological constraints on two decaying dark matter models in
light of BOSS-DR12 data analyzed under the Effective Field Theory of
Large-Scale Structures (EFTofLSS) formalism, together with Planck, Pantheon and
other BOSS measurements of the baryonic acoustic oscillation (BAO). In the
first model, a fraction $f_{\rm dcdm}$ of cold dark matter (CDM) decays into
dark radiation (DR) with a lifetime $\tau$. In the second model (recently
suggested as a potential resolution to the $S_8$ tension), all the CDM decays
with 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 the
DR. Using numerical codes from the recent literature, we perform the first
calculation of the mildly non-linear (matter and galaxy) power spectra with the
EFTofLSS for these two models. In the case of DR products, we obtain the
constraints $f_{\rm dcdm}\lesssim0.022$ (95\% C.L.) for lifetimes shorter than
the age of the universe, and $\tau/f_{\rm dcdm} \gtrsim 250$ Gyr in the
long-lived regime assuming $f_{\rm dcdm}\to1$. We show that Planck data
contributes the most to these constraints, with EFTofBOSS providing a marginal
improvement over conventional BAO and redshift space distortions ($f\sigma_8$)
data. In the case of DR and WDM decay products, we find that EFTofBOSS data
significantly 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 while
lowering $S_8$ 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 exquisite
constraints on such models.
