Paper · Sep 24, 2024
Nonassicative cosmological solitonic R-flux deformations in gauge gravity and G. Perelman geometric flow thermodynamics
As on arXiv
Abstract
We elaborate on a model of nonassociative and noncommutative gauge gravity for the de Sitter gauge group embedding extensions of the affine structure group and the Poincaré group . In string theory, such nonassociative gauge gravity theories are determined by star product R-flux deformations. They are new avenues to quantum gravity and geometric and quantum information theories. We analyze 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 can't 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 analyze the temperature-like evolution of cosmological constants determined by nonassociative cosmological flows.
Comments: latex2e, 11pt, 18pages
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Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 6A.12Entropy, Information and Diffusion
Entropy along the heat flow, the log-Sobolev inequality and Li–Yau: the ancestors of Perelman’s entropy.
- 6A.13Self-Similar Variables and Monotonicity
Changing variables so that self-similar solutions stand still: convergence to the Gaussian, Giga–Kohn blow-up, Gaussian-weighted monotonicity formulas, frequency functions, and the blow-up logic of Huisken, Struwe and Perelman.
- 6B.16Eigenvalue Problems and Perelman’s λ
Rayleigh quotients and min–max, Faber–Krahn and Cheeger’s inequality, ground states of Schrödinger operators, spectral clustering, and the first eigenvalue of −4Δ + R that begins Perelman’s first preprint.