Short answers, pulled from the story.
The Einstein-de Sitter universe is a cosmological model proposed by Albert Einstein and Willem de Sitter in 1932. It describes a flat, matter-only expanding universe with both the cosmological constant and spatial curvature set to zero. In modern terms it corresponds to a flat matter-only Friedmann-Lemaitre-Robertson-Walker metric universe.
The model was a response to Edwin Hubble's discovery of a linear relationship between the redshift of galaxies and their distance. Einstein had already simplified the Friedmann equations by removing the cosmological constant; de Sitter and Einstein then went further by also assuming zero spatial curvature, arriving at the simplest possible expanding-universe model.
The model places the current age of the universe at two thirds of the Hubble time, derived from the specific way the size of an Einstein-de Sitter universe evolves with time.
The theory of cosmic inflation predicted that the curvature of the universe should be very close to zero, which matched the Einstein-de Sitter assumption exactly. This connection made the model the natural framework for cold dark matter theories, which were built around an initial matter budget of roughly 95 percent cold dark matter and 5 percent baryons.
Galaxy clustering data and Hubble constant measurements created problems in the 1990s. The 1998 discovery of the accelerating universe, followed by cosmic microwave background observations and galaxy redshift surveys in 2000-2003, confirmed that dark energy makes up roughly 70 percent of the present energy density, ruling out a zero cosmological constant.
It remains a good approximation to the real universe at redshifts between roughly 300 and 2, covering the period after the radiation-dominated era but before dark energy became significant. Cosmologists still apply it when studying structure formation during that epoch.