Exploring the evolution of structure growth in the universe with field-fluid interactions through dynamical stability analysis

Anirban Chatterjee; Abhijit Bandyopadhyay; Debasish Majumdar

doi:10.1140/epjc/s10052-025-13856-0

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 141
https://doi.org/10.1140/epjc/s10052-025-13856-0

Regular Article - Theoretical Physics

Exploring the evolution of structure growth in the universe with field-fluid interactions through dynamical stability analysis

Anirban Chatterjee¹^a, Abhijit Bandyopadhyay² and Debasish Majumdar²

¹ Institute of Fundamental Physics and Quantum Technology, Department of Physics, School of Physical Science and Technology, Ningbo University, 315211, Ningbo, Zhejiang, China
² Department of Physics, Ramakrishna Mission Vivekananda Educational and Research Institute, Belur Math, 711202, Howrah, West Bengal, India

^a iitkanirbanc@gmail.com, anirbanchatterjee@nbu.edu.cn

Received: 9 August 2024
Accepted: 23 January 2025
Published online: 4 February 2025

Abstract

We investigate an interacting quintessence dark energy – dark matter scenario and its impact on structure formation by analyzing the evolution of scalar perturbations. The interaction is introduced by incorporating a non-zero source term into the continuity equations of the two sectors (with opposite signs), modeled as ${\bar{Q}}_{0} \equiv α {\bar{ρ}}_{m} (H + κ \dot{ϕ})$ $\bar{Q}_0 \equiv \alpha \bar{\rho }_\textrm{m}(H + \kappa \dot{\phi })$ . The coupling parameter $α$ $\alpha$ and the parameter $λ$ $\lambda$ involved in quintessence potential $V (ϕ) = V_{0} e^{- λ κ ϕ}$ $V(\phi ) = V_0e^{-\lambda \kappa \phi }$ , play crucial roles in governing the dynamics of evolution examined within the present framework. The cosmic evolution, within this context, is depicted as a first-order autonomous system of equations involving appropriately chosen dynamical variables. We analyzed the associated stability characteristics and growth rate of perturbations, and obtained domains in the ( $α - λ$ $\alpha -\lambda$ ) parameter space for which fixed points can exhibit stable and non-phantom accelerating solutions. Depending on its magnitude, the coupling parameter $α$ $\alpha$ has the potential to change the characteristics of certain critical points, altering them from attractors to repellers. This model effectively captures the evolutionary features of the universe across its various phases at both the background and perturbation levels. The issue of cosmic coincidence can also be addressed within the framework of this model. We also observed that for a moderate strength of coupling, the growth rate of matter perturbation extends into the distant future.

© The Author(s) 2025

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