An analytical late-Universe approach to the weaving of modern cosmology

Combining cosmological probes has consolidated the standard cosmological model with percent precision, but some tensions have recently emerged when certain parameters are estimated from the local or primordial Universe. The origin of this behaviour is still under debate, however, it is crucial to study as many probes as possible to cross-check the results with independent methods and provide additional pieces of information to the cosmological puzzle. In this work, by combining several late-Universe probes (0$<z<$10), namely, Type Ia SuperNovae, Baryon Acoustic Oscillations, Cosmic Chronometers and Gamma-Ray Bursts, we aim to derive cosmological constraints independently of local or early-Universe anchors. To test the standard cosmological model and its various extensions, considering an evolving Dark Energy Equation of State and the curvature as a free parameter, we analyse each probe individually and all their possible permutations. Assuming a flat $\Lambda$CDM model, the full combination of probes provides $H_0=67.2^{+3.4}_{-3.2}$ km s$^{-1}$ Mpc$^{-1}$ and $\Omega_m=0.325\pm0.015$ (68$\%$ C.L.). Considering a flat $w$CDM model, we measure $w_0=-0.91^{+0.07}_{-0.08}$ (68$\%$ C.L.), while by relaxing the flatness assumption ($\Lambda$CDM model, 95$\%$ C.L.) we obtain $\Omega_k=0.125^{+0.167}_{-0.165}$. Finally, we analytically characterize the degeneracy directions and the relative orientation of the probes' contours. By calculating the Figure-of-Merit, we quantify the synergies among independent methods, estimate the constraining power of each probe and identify which provides the best contribution to the inference process. Pending the new cosmological surveys, this study confirms the exigency for new emerging probes in the landscape of modern cosmology.