Starobinsky Inflation and Dark Energy and Dark Matter Effects from Quasicrystal Like Spacetime Structures

TL;DR

This paper explores how quasicrystal-like spacetime structures in modified gravity theories can model inflation, dark energy, and dark matter effects through exact solutions with inhomogeneous and anisotropic properties.

Contribution

It introduces a geometric framework for modeling quasicrystal-like spacetime structures in modified gravity, linking them to inflation and dark sector phenomena.

Findings

Exact cosmological solutions with quasicrystal-like structures are constructed.

Modeling of inflationary and acceleration phases via off-diagonal metrics.

Potential explanations for dark energy and dark matter effects through spacetime deformations.

Abstract

The goal of this work on mathematical cosmology and geometric methods in modified gravity theories, MGTs, is to investigate Starobinsky-like inflation scenarios determined by gravitational and scalar field configurations mimicking quasicrystal, QC, like structures. Such spacetime aperiodic QCs are different from those discovered and studied in solid state physics but described by similar geometric methods. We prove that an inhomogeneous and locally anisotropic gravitational and matter field effective QC mixed continuous and discrete "aether" can be modeled by exact cosmological solutions in MGTs and Einstein gravity. The coefficients of corresponding generic off-diagonal metrics and generalized connections depend (in general) on all spacetime coordinates via generating and integration functions and certain smooth and discrete parameters. Imposing additional nonholonomic constraints, prescribing symmetries for generating functions and solving the boundary conditions for integration functions and constants, we can model various nontrivial torsion QC structures or extract cosmological Levi--Civita configurations with diagonal metrics reproducing de Sitter (inflationary) like and other types homogeneous inflation and acceleration phases. Finally, we speculate how various dark energy and dark matter effects can be modeled by off-diagonal interactions and deformations of a nontrivial QC like gravitational vacuum structure and analogous scalar matter fields.