Dynamical Stability of the Power Law K-essence Dark Energy Model with a New Interaction

TL;DR

This paper studies a power law K-essence dark energy model with a new interaction term, analyzing its stability and cosmological implications, including a novel attractor solution that aligns with observations and addresses the Coincidence Problem.

Contribution

It introduces a new interaction in the power law K-essence dark energy model and identifies a novel stable attractor solution with significant cosmological implications.

Findings

Discovery of a new stable attractor solution with specific dark energy parameters.

The attractor solution aligns with observational data and alleviates the Coincidence Problem.

Analysis of the model's critical points and their cosmological significance.

Abstract

We investigate the cosmological evolution of the power law K-essence dark energy (DE) model $F(X)= -\sqrt{X} + X$ with a new interaction $Q = \alpha\rho _m\rho _{\phi }H^{-1}$ in FRWL spacetime. The evolution behavior of dark energy under this interaction is analyzed by using dynamical systems method, and ten critical points are obtained. Among those critical points, a new stable point, which we called Scaling-like dark energy(DE) solution, is very important and interesting. The cosmological meaning of this attractor is different from the Scaling solution and dark energy dominated solution. For some value of model parameters, the universe will evolve to the attractor solution with the dark energy density parameter $\Omega_{\phi}=0.682946$ and the the equation of state $w_{\phi}=-0.99$, which can be in good agreement with the observed data, and alleviate the Coincidence Problem.