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

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 $$\bar{Q}_0 \equiv \alpha \bar{\rho }_\textrm{m}(H + \kappa \dot{\phi })$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mover> <mml:mrow> <mml:mi>Q</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>≡</mml:mo> <mml:mi>α</mml:mi> <mml:msub> <mml:mover> <mml:mrow> <mml:mi>ρ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mtext>m</mml:mtext> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>H</mml:mi> <mml:mo>+</mml:mo> <mml:mi>κ</mml:mi> <mml:mover> <mml:mi>ϕ</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . The coupling parameter $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> and the parameter $$\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> </mml:math> involved in quintessence potential $$V(\phi ) = V_0e^{-\lambda \kappa \phi }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>V</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>V</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mi>λ</mml:mi> <mml:mi>κ</mml:mi> <mml:mi>ϕ</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , 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 ( $$\alpha -\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>-</mml:mo> <mml:mi>λ</mml:mi> </mml:mrow> </mml:math> ) parameter space for which fixed points can exhibit stable and non-phantom accelerating solutions. Depending on its magnitude, the coupling parameter $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> 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.