Cyclic model

A cyclic model, also called an oscillating model, describes a universe that goes through endless or indefinite repeating cycles. In one early version, briefly considered by Albert Einstein in 1930, the universe would undergo an eternal series of oscillations: each cycle starts with a Big Bang, expands for a time, then collapses under gravity in a Big Crunch, leading to a Big Bounce into the next cycle.

Alexander Friedmann first proposed the oscillating universe theory in 1922. However, Richard C. Tolman showed in 1934 that these early models failed due to the cyclic problem: the second law of thermodynamics demands that entropy always increases. This means each successive cycle becomes longer and larger. Going backward in time, earlier cycles become shorter and smaller, ultimately leading back to a Big Bang rather than replacing it. This puzzle persisted for decades until the early 2000s, when the discovery of dark energy offered new hope for a consistent cyclic cosmology. A 2011 survey of 200,000 galaxies over 7 billion years confirmed that dark energy is accelerating the universe's expansion.

One newer cyclic model is the brane cosmology model, based on the earlier ekpyrotic model, proposed in 2001 by Paul Steinhardt and Neil Turok. It describes a universe that explodes into existence repeatedly. This theory might explain why the cosmological constant—a repulsive energy accelerating the universe—is far smaller than standard Big Bang predictions. Another cyclic model, relying on phantom energy, was proposed in 2007 by Lauris Baum and Paul Frampton. Other examples include conformal cyclic cosmology and loop quantum cosmology.

Cyclic models regained attention by the mid-2020s, when tensions between Lambda-CDM predictions and DESI mapping observations about dynamic dark energy cast doubt on the universe's final fate, leaving the possibility of a Big Bounce open.

**Steinhardt–Turok model** In this model, two parallel orbifold planes or M-branes collide periodically in a higher-dimensional space. Our visible four-dimensional universe lies on one brane. Collisions correspond to a reversal from contraction to expansion—a Big Crunch immediately followed by a Big Bang. Matter and radiation we see today were generated in the most recent collision, shaped by quantum fluctuations created before the branes collided. After billions of years, the universe reached its current state; after more billions, it will begin contracting again. Dark energy acts as a force between the branes, solving the monopole, horizon, and flatness problems. Cycles can continue indefinitely into past and future, and the solution is an attractor, offering a complete cosmic history.

Tolman showed earlier cyclic models fail due to thermodynamic heat death. This newer model avoids that by having net expansion each cycle, preventing entropy buildup. However, major open issues remain: string theorists do not fully understand colliding branes, and it is unknown whether the scale-invariant spectrum survives the big crunch. Also, like cosmic inflation, the general character of the required forces is known, but no particle physics candidate exists.

**Baum–Frampton model** This 2007 model assumes phantom energy, an exotic dark energy with negative kinetic energy that would normally cause a Big Rip. This occurs if the equation of state parameter satisfies a specific condition (for energy density and pressure), unlike the Steinhardt–Turok model. In Baum–Frampton, a septillionth of a second (or less) before the would-be Big Rip, a turnaround happens, and only one causal patch is retained as our universe. This patch contains no quarks, leptons, or force carriers—only dark energy—so its entropy vanishes. The contraction of this much smaller universe proceeds adiabatically with constant zero entropy and no matter, including no black holes, which disintegrated before turnaround.

The idea that the universe "comes back empty" is central to this model, avoiding problems like excessive structure formation, black hole proliferation, and phase transitions (such as QCD and electroweak symmetry restoration) that would cause an unwanted premature bounce to avoid violating the second law. The condition may be logically necessary for an infinitely cyclic cosmology due to the entropy problem. Still, many technical calculations are needed to confirm consistency. While the model borrows from string theory, it does not require strings or higher dimensions, though such speculative tools may help investigate internal consistency.