An efficient one-loop EFTofLSS framework for Vainshtein-screened Horndeski gravity

We present an extension of $\mathtt{\text{PyBird}}$ for one-loop large-scale structure analyses of modified gravity models. We implement support for quasi-static, Vainshtein-screened luminal Horndeski models (in EFTofDE and covariant formalisms) and nDGP, and replace the Green’s function approach with a direct ODE method for computing the exact time-dependent functions entering the perturbation kernels. The new implementation improves computational efficiency while maintaining numerical consistency with the standard approach, and we validate the resulting one-loop matter power spectrum against $N$-body simulations for the ${\alpha }_i\propto {\mathrm{\Omega }}_{\mathrm{D}\mathrm{E}}$ parametrization. We apply this framework to constrain the ${\alpha }_i\propto a^3$ and ${\alpha }_i\propto {\mathrm{\Omega }}_{\mathrm{D}\mathrm{E}}$ parametrizations using Planck CMB, BOSS full-shape, and DESI DR2 BAO data, finding that full-shape information significantly tightens the constraints. We further showcase the pipeline for the cubic Galileon and nDGP models, demonstrating its applicability beyond the phenomenological amplitude parametrizations to covariant modified-gravity theories. Finally, we assess the impact of the Einstein–de Sitter approximation and find that exact time dependence can be retained at modest computational cost, which may become relevant for future large-scale structure surveys.