Friedmann Models and the Universe's Ultimate Fate

Key Insight

The revelation of an expanding universe challenged the long-held belief in a static cosmos, a view even Newton and Einstein initially supported. Newton should have deduced that a static universe would inevitably collapse under its own gravity. Einstein, in 1915, notably modified his general theory of relativity by introducing a 'cosmological constant' – an inherent 'antigravity' force within space-time – specifically to counteract gravitational attraction and maintain a static universe. However, Russian physicist Alexander Friedmann, in 1922, years before Hubble's discovery, derived solutions for a non-static universe based on two simple assumptions: the universe appears uniform in all directions, and this uniformity is true from any vantage point.

Friedmann's mathematical models, based on these assumptions, describe three possible futures for the universe. The first model depicts a universe expanding slowly enough that the mutual gravitational attraction between galaxies eventually halts the expansion, causing it to slow, stop, and then contract, ultimately collapsing back on itself. In this scenario, space is finite but without boundaries, conceptually similar to the surface of the Earth. Time in this model is also finite, having a definite beginning and end.

The second and third Friedmann models describe a universe that expands forever. In the second type, the universe expands so rapidly that gravity can never overcome its outward momentum, leading to perpetual expansion with galaxies continuously accelerating away from each other; in this case, space is infinite and curved like a saddle. The third model represents a critical balance, where the universe expands just fast enough to avoid recollapse; it expands forever, but the expansion rate steadily decreases, asymptotically approaching zero, with space being flat and infinite. Determining which model describes our universe hinges on its current expansion rate and average density. If the density is below a critical value, the universe expands forever; if above, it recollapses. Current data, including 'dark matter,' suggests the density is about one tenth of the critical value, implying perpetual expansion, though any potential recollapse is at least 10 thousand million years in the distant future.