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Phase space analysis in $f(R,L_{m})$ gravity with scalar field

Y. Kalpana Devi, Rahul Bhagat, B. Mishra

Abstract

In this work, we investigate the cosmological dynamics of the $f(R, \mathcal{L}_m)$ gravity framework with a particular focus on the contributions of the scalar field. Considering a functional form that includes linear and exponential dependence on the matter Lagrangian, we perform a detailed dynamical system analysis by introducing appropriate dimensionless variables and constructing the corresponding autonomous system. The critical points are obtained and analyzed, and due to their non-hyperbolic nature, center manifold theory is employed to determine their stability. The analysis reveals the existence of matter-dominated and accelerated phases of the Universe, along with a transition from a decelerated to an accelerated expansion. We further extend the model by incorporating a minimally coupled generalized scalar field with a kinetic term and an exponential self-interacting potential, which enriches the dynamical behavior and leads to stable late-time attractor solutions. The evolution of cosmological parameters, including the deceleration parameter and the effective equation of state, indicates that the model approaches a de Sitter-like phase at late times. These results demonstrate that the $f(R, \mathcal{L}_m)$ gravity framework, with scalar field extensions, provides a viable mechanism to explain the late-time acceleration of the Universe without invoking a cosmological constant.

Phase space analysis in $f(R,L_{m})$ gravity with scalar field

Abstract

In this work, we investigate the cosmological dynamics of the gravity framework with a particular focus on the contributions of the scalar field. Considering a functional form that includes linear and exponential dependence on the matter Lagrangian, we perform a detailed dynamical system analysis by introducing appropriate dimensionless variables and constructing the corresponding autonomous system. The critical points are obtained and analyzed, and due to their non-hyperbolic nature, center manifold theory is employed to determine their stability. The analysis reveals the existence of matter-dominated and accelerated phases of the Universe, along with a transition from a decelerated to an accelerated expansion. We further extend the model by incorporating a minimally coupled generalized scalar field with a kinetic term and an exponential self-interacting potential, which enriches the dynamical behavior and leads to stable late-time attractor solutions. The evolution of cosmological parameters, including the deceleration parameter and the effective equation of state, indicates that the model approaches a de Sitter-like phase at late times. These results demonstrate that the gravity framework, with scalar field extensions, provides a viable mechanism to explain the late-time acceleration of the Universe without invoking a cosmological constant.

Paper Structure

This paper contains 6 sections, 55 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The gravity
  3. Dynamical system analysis in $f(R,\mathcal{L}_m)$ gravity
  4. The gravity with scalar field
  5. Dynamical System Analysis in generalized $f(R, \mathcal{L}_m)$ Gravity with self-interacting exponential potential
  6. Conclusion

Figures (4)

  • Figure 1: Phase portrait for the dynamical system of the critical point $C_1$(Left Panel) and critical point $C_2$(Right Panel).
  • Figure 2: Evolution of density parameters ( Left Panel) and deceleration and EoS parameter ( Right Panel) in redshift.
  • Figure 3: Phase portrait for the dynamical system of the critical point $C_1$(Left Panel) and critical point $C_2$(Right Panel).
  • Figure 4: Evolution of density parameters ( Left Panel) and deceleration and EoS parameter ( Right Panel) in redshift.