https://doi.org/10.1140/epjc/s10052-024-13001-3
Regular Article - Theoretical Physics
Nonmetric geometric flows and quasicrystalline topological phases for dark energy and dark matter in 
cosmology
1
SRTV-Studioul TVR Iaşi and University Appolonia, 2 Muzicii street, 700399, Iasi, Romania
2
Department of General and Theoretical Physics, Eurasian National University, 010000, Astana, Kazakhstan
3
Department of Information Technologies and Computer Physics, Yu. Fedkovych Chernivtsi National University 2, 58012, Chernivtsi, Ukraine
4
Department of Applied Mathematics, Lviv Polytechnic National University, Stepan Bandera street, 12, 79000, Lviv, Ukraine
5
Department of Physics, California State University at Fresno, 93740, Fresno, CA, USA
6
Yu. Fedkovych Chernivtsi National University 2, 58012, Chernivtsi, Ukraine
7
Center for Advanced Studies, Ludwig-Maximilians-Universität, Seestrasse 13, 80802, Munich, Germany
8
Department of Physics, Kocaeli University, 41380, Izmit, Turkey
d sergiu.vacaru@fulbrightmail.org, sergiu.vacaru@gmail.com
Received:
29
February
2024
Accepted:
9
June
2024
Published online:
28
June
2024
We elaborate on nonmetric geometric flow theory and metric-affine gravity with applications in modern cosmology. Two main motivations for our research follow from the facts that (1) cosmological models for f(Q) modified gravity theories, MGTs, are efficient for describing recent observational data provided by the James Webb Space Telescope; and (2) the statistical thermodynamic properties of such nonmetric locally anisotropic cosmological models can be studied using generalizations of the concept of G. Perelman entropy. We derive nonmetric distorted R. Hamilton and Ricci soliton equations in such canonical nonholonomic variables when corresponding systems of nonlinear PDEs can be decoupled and integrated in general off-diagonal forms. This is possible if we develop and apply the anholonomic frame and connection deformation method involving corresponding types of generating functions and generating sources encoding nonmetric distortions. Using such generic off-diagonal solutions (when the coefficients of metrics and connections may depend generically on all spacetime coordinates), we model accelerating cosmological scenarios with quasi-periodic gravitational and (effective) matter fields; and study topological and nonlinear geometric properties of respective dark energy and dark matter, DE and DM, models. As explicit examples, we analyze some classes of nonlinear symmetries defining topological quasicrystal, QC, phases which can modified to generate other types of quasi-periodic and locally anisotropic structures. The conditions when such nonlinear systems possess a behaviour which is similar to that of the Lambda cold dark matter (
CDM) scenario are stated. We conclude that nonmetric geometric and cosmological flows can be considered as an alternative to the CDM concordance models and speculate on how such theories can be elaborated. This is a partner work with generalizations and applications of the results published by Bubuianu, Vacaru et all. EPJC 84 (2024) 211; 80 (2020) 639; 78 (2018) 393; 78 (2018) 969; and CQG 35 (2018) 245009.
© The Author(s) 2024
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
