Precision Cosmology in Modified and Extended Theories of Gravity: an insightful test

Abstract: In this work we present a brief discussion about modified and extended cosmological models using current observational tests. We show that according to these astrophysical samples based in late universe measurements, theories like $f(R)$ and $f(T,B)$ can provide useful interpretation to a dynamical dark energy. At this stage, precision cosmostatistics has also become a well-motivated endeavour by itself to test gravitational physics at cosmic scales and these analyses can be employed to test the viability and future constrains over specific cosmological models of these theories of gravity, making them a good approach to propose an alternative path from the standard $\Lambda$CDM scenario.