  I present the first constraints on decaying cold dark matter (DCDM) models
thanks to the effective field theory of large-scale structure (EFTofLSS)
applied to BOSS-DR12 data. I consider two phenomenological models of DCDM: i) a
model where a fraction $f_{\rm dcdm}$ of cold dark matter (CDM) decays into
dark radiation (DR) with a lifetime $\tau$; ii) a model (recently suggested as
a potential resolution to the $S_8$ tension) where 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. I
discuss the implications of the EFTofLSS constraints for the DCDM model
suggested to resolve the $S_8$ tension.
