Probing nonlinear structure formation beyond $\Lambda$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 $\Lambda$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 $\varepsilon_f$ and $\varepsilon_{d_{\gamma}}$, 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 \texttt{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 $\sim 7\%$ constraints on $\varepsilon_f$ and $\sim 57\%$ constraints on $\varepsilon_{d_{\gamma}}$. For the PT Challenge, whose survey volume is about 100 times larger, we reach $\sim 1\%$ precision on $\varepsilon_f$ and $\sim 25\%$ on $\varepsilon_{d_{\gamma}}$, including the bispectrum quadrupole in the analysis. Our results underscore the complementary roles of $\varepsilon_f$ and $\varepsilon_{d_{\gamma}}$ 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 $\Lambda$CDM with existing and upcoming galaxy surveys.