Cosmology with VLT spectrographs in 2030s

In 2030s, cosmologist will be working with the vast cosmological datasets produced by Euclid, DESI, and Vera Rubin Observatory, and many others. The incredible amount of available data will allow precise measurements of key cosmological parameters and possibly answer some famous tensions of contemporary cosmology. At this point, we might have a new cosmological paradigm with new degrees of freedom to explain the observed phenomena. Investigating variations in the values of fundamental constants is one particularly promising and exciting method of constraining models beyond LCDM, and will be used in combination with other cosmological probes to put tight bounds on viable models. Measurements of fundamental constants in the early universe have demanding requirements (collecting area, spectral resolution, wavelength calibration) that can only be achieved on large telescopes such as the VLT. I will discuss why the VLT will continue to be extremely useful for this line of research, extending into and beyond 2030s and the era of the ELT, with a particular focus on ESPRESSO and the proposed multi-object high-resolution spectrograph, HRMOS.