Cosmology and Fundamental Physics with the ELT-ANDES Spectrograph

State-of-the-art 19th century spectroscopy led to the discovery of quantummechanics, and 20th century spectroscopy led to the confirmation of quantumelectrodynamics. State-of-the-art 21st century astrophysical spectrographs,especially ANDES at ESO's ELT, have another opportunity to play a key role inthe search for, and characterization of, the new physics which is known to beout there, waiting to be discovered. We rely on detailed simulations andforecast techniques to discuss four important examples of this point: big bangnucleosynthesis, the evolution of the cosmic microwave background temperature,tests of the universality of physical laws, and a real-time model-independentmapping of the expansion history of the universe (also known as the redshiftdrift). The last two are among the flagship science drivers for the ELT. Wealso highlight what is required for the ESO community to be able to play ameaningful role in 2030s fundamental cosmology and show that, even if ANDESonly provides null results, such `minimum guaranteed science' will be in theform of constraints on key cosmological paradigms: these are independent from,and can be competitive with, those obtained from traditional cosmologicalprobes.