A study of interacting NTADE and SMHDE models via cosmological parameters within rastall gravity

This article explores the characteristics of interacting new Tsallis agegraphic dark energy (NTADE) and Sharma–Mittal holographic dark energy (SMHDE) models in a flat FLRW universe within Rastall gravity (RG). To check the viability of these models and to distinguish them, we develop important cosmological parameters including equation of state (EoS) parameter, deceleration parameter q, square speed of sound, statefinder pair and Om(z) diagnostic. By constraining the different parameters for both dark energy (DE) models, it is observed that: EoS parameter indicates phantom-like behavior, deceleration parameter is showing a phase transition from decelerating to accelerating phase. The (j, s) plane is indicating a rich behavior as it shows different DE eras like quintessence, phantom and Chaplygin gas for both models depending upon interacting term \(d^{2}\) $d^2$ , parameter \(\delta \) $\delta$ and Rastall parameter \(\lambda \) $\lambda$ . The \(\omega _{D}-\omega ^{'}_{D}\) ${\omega }_D-\omega _D^{_{}^{\prime }}$ pair is indicating freezing region for NTADE but for SMHDE it initially falls in freezing region then move towards thawing region. We also check stability of NTADE/SMHDE models through the graphical interpretation of square speed of sound.