The big crunch
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The Big Crunch: A Comprehensive Overview
Introduction to the Big Crunch Theory
The Big Crunch is a theoretical scenario in cosmology where the expansion of the universe eventually reverses, leading to a collapse back into a singularity. This concept is rooted in Einstein's general theory of relativity, which predicts that space-time began at the Big Bang and could end at a Big Crunch if the universe's expansion halts and reverses .
Quantum Descriptions and String Theory
Recent studies have explored the Big Crunch within the framework of string theory and supergravity. One significant finding is that smooth asymptotically anti-de Sitter initial data can evolve into a Big Crunch singularity in a low-energy supergravity limit of string theory. This suggests that the Big Crunch could be described fully by a dual conformal field theory, providing a quantum perspective on cosmological singularities . Additionally, the dual gauge theory description of cosmological solutions indicates that the Big Bang and Big Crunch singularities are related by S-duality symmetry, making them nonsingular in the N=4 super Yang-Mills theory .
M Theory and Big Crunch/Big Bang Transition
M theory offers another intriguing perspective on the Big Crunch. It posits that the transition from a Big Crunch to a Big Bang can be modeled as the collision of two empty orbifold planes. This model shows that $p$-brane states, including string theory gravitons, can propagate smoothly across the transition, suggesting that interactions remain well-behaved due to the smooth evolution of fields and the diminishing string coupling at the crunch . This contrasts with traditional general relativity descriptions, which often predict chaotic behaviors like Kasner or mixmaster dynamics.
Weyl-Invariant Theories and Geodesic Completeness
Theories with scalar fields coupled to gravity, such as the standard model, can be adapted to a Weyl-invariant framework. This adaptation allows for the tracing of classical cosmological evolution through the Big Crunch to Big Bang transition. By identifying finite, Weyl-invariant conserved quantities, researchers have shown that it is possible to construct a complete set of geodesics that pass continuously through the transition, challenging previous conclusions about the geodesic incompleteness of such models .
Big Bang-Big Crunch Algorithms in Optimization
Beyond theoretical physics, the Big Bang-Big Crunch (BB-BC) algorithm has been applied to optimization problems. This metaheuristic, inspired by the universe's evolution, involves creating a population of random initial solutions (Big Bang) and then shrinking them into an elite solution (Big Crunch). Enhanced versions of this algorithm, such as the Differential Big Bang-Big Crunch (DBB-BC) and chaotic-based BB-BC, have shown significant improvements in finding global solutions for various mathematical and practical design problems 368.
Conclusion
The Big Crunch remains a compelling theoretical endpoint for the universe, with significant implications in both cosmology and applied mathematics. Advances in string theory, M theory, and Weyl-invariant models provide deeper insights into the nature of cosmological singularities and the potential for a quantum description of the universe's ultimate fate. Additionally, the application of Big Bang-Big Crunch algorithms in optimization highlights the interdisciplinary impact of these cosmological concepts.
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