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

We present an extension of \texttt{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 $\alpha_i\propto\Omega_{\rm DE}$ parametrization. We apply this framework to constrain the $\alpha_i \propto a^3$ and $\alpha_i \propto \Omega_{\rm DE}$ 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.