From the Intergalactic to the Interstellar Scales -- EQUALS: a High-resolution Legacy Survey of Gas in the Distant Universe Using ESPRESSO

Understanding how the Universe evolved from diffuse primordial gas into the rich cosmic web we observe today is one of the great challenges of modern astrophysics. Quasar absorption lines - the imprints left by intervening gas on the light from distant quasars - provide key diagnostics of many aspects of this investigation, ranging from fundamental physics to cosmology and galaxy formation. The unprecedented combination of extremely precise wavelength calibration, high spectral resolution and high sensitivity of the Echelle SPectrograph for Rocky Exoplanet and Stable Spectroscopic Observations (ESPRESSO) has finally enabled observations that will further constrain both state-of-the-art cosmological simulations of galaxy evolution and theoretical stellar nucleosynthetic yields. In this article, we present the ESPRESSO Quasar Absorption Line Survey (EQUALS), an ESO Large Programme, designed to tackle several outstanding questions from constraining the properties of dark matter at the smallest scales probed by the Lyman-alpha forest to determining the temperature of the intergalactic medium at z ~ 4 and precisely quantifying the chemical contributions of stellar populations in the early Universe. EQUALS will provide a legacy sample of deep spectra to showcase ESPRESSO capabilities to the quasar absorption line community whilst providing epoch measurements for the key science goals of upcoming spectroscopic instrumentation on the next generations of telescopes.