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. ©2017 Keywords: complexity; symmetry; virtual particles; antiscreening; renormalization group; fractional calculus; Lifshitz ordering; dark matter