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Accelerating behavior from dynamical system analysis parameters

Rahul Bhagat, B. Mishra

TL;DR

The paper investigates late-time cosmic acceleration within a symmetric teleparallel gravity framework by proposing a logarithmic $f(Q)$ model. It derives the modified field equations, reformulates them into an autonomous dynamical system, and constrains the model using MCMC with Cosmic Chronometers and Pantheon$^+$ Type Ia Supernova data, revealing quintessence-like behavior today and a de Sitter attractor at late times. The results provide tight parameter bounds and show that the model closely tracks $\Lambda$CDM in the future, supporting $f(Q)$ gravity as a viable geometric alternative to dark energy. Overall, the work demonstrates that a logarithmic modification of nonmetricity can reproduce the observed expansion history and offers a robust framework for testing geometric gravity against current cosmological data.

Abstract

We have performed the dynamical system analysis to obtain the critical point in which, the value of the geometric and dynamical parameters satisfy the late-time cosmic behavior of the Universe. At the outset, the modified Friedmann equations have been reformulated into a system of coupled differential equations to ensure that the minimal set of equations required for a second-order $f(Q)$ gravity. Then these equations are solved numerically to constrain the parameters with Markov Chain Monte Carlo (MCMC) techniques. Cosmic Chronometers (CC) and high-precision Pantheon$^+$ Type Ia Supernovae datasets are used to constrain the parameters. The evolution of key cosmological parameters indicates that the model exhibits quintessence-like behavior at present, with a tendency to converge towards the $Λ$CDM model at late-times. The dynamic system analysis provided the critical points that correspond to different phases of the Universe, which are analyzed in detail. The existence of a stable de Sitter attractor confirms the accelerating behavior of the model.

Accelerating behavior from dynamical system analysis parameters

TL;DR

The paper investigates late-time cosmic acceleration within a symmetric teleparallel gravity framework by proposing a logarithmic model. It derives the modified field equations, reformulates them into an autonomous dynamical system, and constrains the model using MCMC with Cosmic Chronometers and Pantheon Type Ia Supernova data, revealing quintessence-like behavior today and a de Sitter attractor at late times. The results provide tight parameter bounds and show that the model closely tracks CDM in the future, supporting gravity as a viable geometric alternative to dark energy. Overall, the work demonstrates that a logarithmic modification of nonmetricity can reproduce the observed expansion history and offers a robust framework for testing geometric gravity against current cosmological data.

Abstract

We have performed the dynamical system analysis to obtain the critical point in which, the value of the geometric and dynamical parameters satisfy the late-time cosmic behavior of the Universe. At the outset, the modified Friedmann equations have been reformulated into a system of coupled differential equations to ensure that the minimal set of equations required for a second-order gravity. Then these equations are solved numerically to constrain the parameters with Markov Chain Monte Carlo (MCMC) techniques. Cosmic Chronometers (CC) and high-precision Pantheon Type Ia Supernovae datasets are used to constrain the parameters. The evolution of key cosmological parameters indicates that the model exhibits quintessence-like behavior at present, with a tendency to converge towards the CDM model at late-times. The dynamic system analysis provided the critical points that correspond to different phases of the Universe, which are analyzed in detail. The existence of a stable de Sitter attractor confirms the accelerating behavior of the model.

Paper Structure

This paper contains 8 sections, 38 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Field Equations of $f(Q)$ gravity
  3. Logarithmic f(Q) Model
  4. Observational Analysis and the Results
  5. MCMC Result
  6. Cosmological Parameters
  7. Phase Space Analysis: Fixed Points and Late-Time Behavior
  8. Results and Discussions

Figures (7)

  • Figure 1: The contour plots for 32 points of CC sample, 1701 light curves from Pantheon$^+$ dataset and combine CC+Pantheon$^+$ dataset upto 2$-\sigma$ errors for the parameters $H_0$, $\Omega_{m_0}$, $\alpha$ and $\beta$.
  • Figure 2: Evolution of Hubble parameter (Top Panel) and distance modulus parameter (Bottom Panel) for the model and $\Lambda$CDM.
  • Figure 3: Evolution of Cosmological parameters for observational Dataset (Upper Panel for CC, Middle Panel for Pantheon$^+$ and Lower Panel for CC+Pantheon$^+$ Dataset) and dotted lines show it comparison to GR with a positive cosmological constant.
  • Figure 4: Behavior of state finder parameter.
  • Figure 5: Plot of the Age of the Universe in Gyr.
  • ...and 2 more figures