We present limits on the parameters of the o$Lambda$CDM, $w_0$CDM, and $w_0 w_a$CDM models obtained from the joint analysis of the full-shape, baryon acoustic oscillations (BAO), big bang nucleosynthesis (BBN) and supernovae data. Our limits are fully independent of the data on the cosmic microwave background (CMB) anisotropies, but rival the CMB constraints in terms of parameter error bars. We find the spatial curvature consistent with a flat universe $Omega_k=-0.043_{-0.036}^{+0.036}$ ($68%$ C.L.); the dark-energy equation of state parameter $w_0$ is measured to be $w_0=-1.031_{-0.048}^{+0.052}$ ($68%$ C.L.), consistent with a cosmological constant. This conclusion also holds for the time-varying dark energy equation of state, for which we find $w_0=-0.98_{-0.11}^{+0.099}$ and $w_a=-0.33_{-0.48}^{+0.63}$ (both at $68%$ C.L.). The exclusion of the supernovae data from the analysis does not significantly weaken our bounds. This shows that using a single external BBN prior, the full-shape and BAO data can provide strong CMB-independent constraints on the non-minimal cosmological models.
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