Explore the cosmic web's role in probing inflationary physics through this 23-minute conference talk by Nathan Carlson from CITA. Delivered at the "Co-evolution of the Cosmic Web and Galaxies across Cosmic Time" conference hosted by the Kavli Institute for Theoretical Physics, delve into how the universe's matter distribution framework connects galactic properties to cosmology. Examine the effects of the cosmic web on galaxies and vice versa, covering topics such as observational estimation in surveys, forecasts for the thermal web at high redshifts, early galaxy and quasar properties within the web, revised galaxy formation theories, and implications for cosmology and structure formation. Gain insights into constraining dark energy's equation of state, primordial non-Gaussianity, and the influence of modified gravity on large-scale structures.