Dynamical stability analysis of entropy corrected cosmic model through zero-point length

Abstract

In this work, we explore a modified entropy expression that incorporates zero-point length correction terms. This approach is inspired by string T-duality, with the zero-point length correction applied to the gravitational potential. The modified form of the Friedmann equations is derived by applying the first law of thermodynamics at the apparent horizon within the framework of the Friedmann–Robertson–Walker (FRW) universe. These modified equations describe the universes evolution with zero-point length corrections embedded in the entropy term. By examining both linear and non-linear interactions, we identify various evolutionary phases of the universe through a detailed analysis of the critical points. Additionally, we investigate the stability and attractor properties of accelerating solutions using eigenvalues and phase space diagrams. Within this framework, different cases of the equation of state parameter such as quintessence, $\Lambda$CDM and phantom regimes, along with dust and radiation are discussed. The evolution plots for these scenarios are analyzed, demonstrating consistency with current observational values of the standard density parameters.