Probing nonlinear structure formation beyond Λ CDM with the LSS bootstrap: A joint power spectrum and bispectrum analysis

We present the first MCMC-derived constraints on the parameters of the Large Scale Structure (LSS) bootstrap, a model-independent framework that captures deviations from $Λ$CDM using symmetry arguments alone. Focusing on modifications to the linear growth rate and to the quadratic perturbation-theory kernel -- quantified by the fractional parameters εf and εd_γ, respectively -- we carry out a joint analysis of the one-loop galaxy power spectrum and the tree-level bispectrum multipoles within the EFTofLSS, employing the PyBird code extended to implement the bootstrap parametrization. We apply this analysis pipeline to two datasets: the BOSS DR12 LRG sample and the large-volume ``PT Challenge'' simulations. For BOSS, combining the power spectrum with the bispectrum monopole yields ~ 7% constraints on εf and ~ 57% constraints on εd_γ. For the PT Challenge, whose survey volume is about 100 times larger, we reach ~ 1% precision on εf and ~ 25% on εd_γ, including the bispectrum quadrupole in the analysis. Our results underscore the complementary roles of εf and εd_γ in separating changes to the background expansion from those affecting nonlinear structure formation, and they show that the LSS bootstrap offers a competitive, model-agnostic method for probing physics beyond $Λ$CDM with existing and upcoming galaxy surveys.