  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.
