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Noncoincidence $f(Q)$-Cosmology with Dark Matter Coupled to Gravity

A. Abebe, P. S. Apostolopoulos, A. Giacomini, G. Leon, F. Moncada, A. Paliathanasis

TL;DR

This work analyzes FLRW cosmology in symmetric teleparallel f(Q) gravity with a nonminimal coupling between dark matter and gravity, using the noncoincidence gauge to reveal a two-scalar-field representation and a Hubble-normalized phase-space framework. It derives the modified Friedmann equations, reconstructs exact solutions (power-law and de Sitter), and formulates a complete dynamical-system analysis that yields equilibrium points A–E and their stability. In the power-law f(Q) case, a de Sitter future attractor arises while a matter-dominated era manifests as a saddle, and scaling solutions may connect to inflationary dynamics; crucially, the DM–gravity coupling enables a viable matter epoch alongside late-time acceleration, unlike uncoupled models. This work highlights the pivotal role of the coupling function in shaping cosmic history within f(Q) gravity and paves the way for perturbation analyses and observational viability studies.

Abstract

We investigate FLRW cosmology in the framework of symmetric teleparallel $f(Q)$ gravity with a nonminimal coupling between dark matter and the gravitational field. In the noncoincidence gauge, the field equations admit an equivalent multi-scalar field representation, which we investigate the phase-space using the Hubble-normalization approach. We classify all stationary points for arbitrary function $f(Q)$ and we discuss the physical properties of the asymptotic solutions. For the power-law theory, we perform a detailed stability analysis and show that the de Sitter solution is the unique future attractor, while the matter-dominated point appears as a saddle point. Moreover, there exist a family of scaling solutions that can be related to inflationary dynamics. In contrast with uncoupled $f(Q)$ models, the presence of the coupling introduces a viable matter-dominated era alongside late-time accelerated expansion. Our study shows that the coupling function plays a crucial role in cosmological dynamics in $f(Q)$ gravity.

Noncoincidence $f(Q)$-Cosmology with Dark Matter Coupled to Gravity

TL;DR

This work analyzes FLRW cosmology in symmetric teleparallel f(Q) gravity with a nonminimal coupling between dark matter and gravity, using the noncoincidence gauge to reveal a two-scalar-field representation and a Hubble-normalized phase-space framework. It derives the modified Friedmann equations, reconstructs exact solutions (power-law and de Sitter), and formulates a complete dynamical-system analysis that yields equilibrium points A–E and their stability. In the power-law f(Q) case, a de Sitter future attractor arises while a matter-dominated era manifests as a saddle, and scaling solutions may connect to inflationary dynamics; crucially, the DM–gravity coupling enables a viable matter epoch alongside late-time acceleration, unlike uncoupled models. This work highlights the pivotal role of the coupling function in shaping cosmic history within f(Q) gravity and paves the way for perturbation analyses and observational viability studies.

Abstract

We investigate FLRW cosmology in the framework of symmetric teleparallel gravity with a nonminimal coupling between dark matter and the gravitational field. In the noncoincidence gauge, the field equations admit an equivalent multi-scalar field representation, which we investigate the phase-space using the Hubble-normalization approach. We classify all stationary points for arbitrary function and we discuss the physical properties of the asymptotic solutions. For the power-law theory, we perform a detailed stability analysis and show that the de Sitter solution is the unique future attractor, while the matter-dominated point appears as a saddle point. Moreover, there exist a family of scaling solutions that can be related to inflationary dynamics. In contrast with uncoupled models, the presence of the coupling introduces a viable matter-dominated era alongside late-time accelerated expansion. Our study shows that the coupling function plays a crucial role in cosmological dynamics in gravity.

Paper Structure

This paper contains 13 sections, 39 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Symmetric Teleparallel Gravity
  3. $f\left( Q\right)$-gravity
  4. Matter Coupled to Gravity
  5. Exact Solutions
  6. Power-law Solution
  7. de Sitter Solution
  8. Cosmological Dynamics
  9. Dimensionless Variables and Dynamical System
  10. Equilibrium Points and Cosmological Interpretation
  11. Linear Stability Analysis
  12. Power-law potential
  13. Conclusions

Figures (3)

  • Figure 1: Qualitative evolution of the physical parameters $\beta\Omega_{m}$ and $w_{eff}$ from numerical similations of the dynamical (\ref{['systA']}) for the power-law potential and for values of the free parameter $\lambda.$
  • Figure 2: Qualitative evolution of the physical parameters $\beta\Omega_{m}$ and $w_{eff}$ from numerical similations of the dynamical (\ref{['systA']}) for the power-law potential and for values of the free parameter $\lambda.$
  • Figure 3: Phase-space portraits for the dynamical system (\ref{['systA']}) with the power-law potential. The red line corresponds to the initial conditions presented in Figs. \ref{['f1']} and \ref{['f2']}.