Nonassociative cosmological solitonic R-flux deformations in gauge gravity and G. Perelman geometric flow thermodynamics


Bubuianu L., Seti J. O., Vacaru S. I., VELİ E.

Annals of Physics, vol.465, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 465
  • Publication Date: 2024
  • Doi Number: 10.1016/j.aop.2024.169689
  • Journal Name: Annals of Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Chemical Abstracts Core, INSPEC, zbMATH
  • Keywords: Cosmological solitonic solutions, Gauge gravity, Modified Perelman's thermodynamics, Nonassociative geometric flows, Nonassociative star product, R-flux deformations
  • Kocaeli University Affiliated: Yes

Abstract

We elaborate on a model of nonassociative and noncommutative gauge gravity for the de Sitter gauge group SO(4,1) embedding extensions of the affine structure group Af(4,1) and the Poincaré group ISO(3,1). Such nonassociative gauge gravity theories are determined by star product R-flux deformations in string theory and can be considered as new avenues to quantum gravity and geometric and quantum information theories. We analyse physically important and geometric thermodynamic properties of new classes of generic off-diagonal cosmological solitonic solutions encoding nonassociative effective sources. Particularly, we focus on modelling by such solutions of locally anisotropic and inhomogeneous dark matter and dark energy structures generated as nonassociative solitonic hierarchies. Such accelerating cosmological evolution scenarios cannot be described in the framework of the Bekenstein–Hawking thermodynamic formalism. This motivates a change in the gravitational thermodynamic paradigm by considering nonassociative and relativistic generalizations of the concept of W-entropy in the theory of Ricci flows. Finally, we compute the corresponding modified G. Perelman's thermodynamic variables and analyse the temperature-like evolution of cosmological constants determined by nonassociative cosmological flows.