One-loop power spectrum corrections in interacting dark energy cosmologies

Interacting Dark Energy (IDE) models offer a promising avenue to explore possible exchanges of energy and momentum between dark matter and dark energy, providing a dynamical extension of the standard $Λ$CDM paradigm. Such interactions modify the growth of cosmic structures, imprinting distinctive signatures on the matter power spectrum that can be tested through large-scale structure (LSS) observations. In this work, we compute the one-loop corrections to the matter power spectrum in IDE models. We then reinterpret these results within the standard framework of the Effective Field Theory of Large-Scale Structure (EFTofLSS), which provides a consistent description of mildly non-linear scales and allows for reliable comparisons with observational data. We investigate two commonly studied forms of the coupling function, $Q$, namely $Q = ξ\mathcal{H} ρ_{\rm m}$ and $Q = ξ\mathcal{H} ρ_{\rm DE}$, and introduce a novel interaction term, $Q = Γ\, ρ_{\rm m} \, ρ_{\rm DE} \, θ_{\rm m}$, characterized by the non-linear coupling constant $Γ$, which links the interaction strength to the velocity divergence of dark matter. This coupling function is proposed to isolate the effects solely of the IDE model on mildly non-linear scales. Using Full-Shape (FS) measurements of the galaxy power spectrum from BOSS DR12, we constrain the interaction rate $Γ$, the cosmological parameters, and the bias parameters. We find $Γ= 0.0039 \pm 0.0082$, which is highly consistent with the $Λ$CDM model. This work opens the possibility of testing IDE models at mildly non-linear scales, potentially providing new insights for this class of models beyond the standard $Λ$CDM framework.