The oscillating universe theory (also known as the cyclic model) was introduced by a Russian scientist A. Friedmann in his seminal papers of 1922 and 1924. Three years after Friedmann’s paper in the Zeitschrift für Physik, an article on the same subject by the Hungarian physicist Cornelius Lanczos appeared in the same journal.
The oscillation theory correlates with the model of an expanding universe and is based on the general relativity equations for a universe with positive curvature (spherical space), which results in the universe expanding for a time and then contracting due to the pull of its gravity, in a perpetual cycle of a Big Bang followed by a Big Crunch. This is then followed by a new cycle of existence.
Time is thus has no beginning and no end: the beginning-of-time paradox is avoided.
Despite the fact that this theory was initially ignored by contemporary physicists and astronomers, the oscillating universe theory was Einstein’s favored model after he rejected his own original model* in the 1930s.
Later, in 1934, the work by Richard C. Tolman showed that the oscillating model is hardly possible because of the cyclic problem: according to the Second Law of Thermodynamics, entropy can only increase. This implies that successive cycles grow longer and larger. Extrapolating back in time, cycles before the present one become shorter and smaller culminating again in a Big Bang and thus not replacing it.
This puzzle remained unsolved for many decades until the early 21st century when the recently discovered dark energy component provided new hope for a consistent cyclic model. In 2011, a five-year survey of 200k galaxies and spanning 7 billion years of cosmic time confirmed that “dark energy is driving our universe apart at accelerating speeds.”
It’s worth mentioning that several new cyclic models were in recent years, they include a Brane cosmology model, Conformal cyclic cosmology and Loop quantum cosmology and a different cyclic model relying on the notion of phantom energy proposed by Lauris Baum and Paul Frampton.
* The model of the universe assumed by Albert Einstein (known as Einsteinian Universe) in his theory of gravity in the early 20th century. He claimed that it was a static, dynamically stable universe which was neither expanding or contracting.