Complexity Phenomena Induced by Novel Symmetry and Symmetry-Breakings with Antiscreening at Cosmological Scales—A Tutorial

Abstract

Complexity phenomena in cosmological evolution due to the scale-running of the propagator coupling constant can yield new insights related to virtual particles and antiscreening effects with dark matter consequences. This idea was developed in accordance with the differential-integral functional formulation of the Wilsonian renormalization group based on the one-particle irreducible scale-dependent effective action for gravitational evolution. In this tutorial communication, we briefly describe the essence of the result with minimal mathematical details and then consider a few simple examples to provide a basic understanding of such an interesting and intriguing complexity process in terms of fractional calculus.

Novel Symmetry and Symmetry-Breaking Induced Complexity in Cosmological Evolution

“…Interesting explicit examples based on fractional calculus will be described to demonstrate this intriguing process [3]. This idea can easily be extended to a variety of dynamic and condensed matter systems.…”