Investigating cosmic evolution through the new agegraphic dark energy model in \(f(Q, {\mathbb {T}})\) gravity

This study explores the reconstruction method within the framework of \(f(Q, {\mathbb {T}})\) gravity by utilising the new agegraphic dark energy (A\(\mathbb {DE)}\) model, where Q represents non-metricity and \({\mathbb {T}}\) is the trace of the energy–momentum tensor. The \(f(Q, {\mathbb {T}})\) new A\({{\mathbb {D}}}{{\mathbb {E}}}\) model is developed through a non-interacting correspondence approach. This theoretical model is then examined in the context of a flat Friedmann–Robertson–Walker (FRW) cosmological framework, which is defined by a power-law scale factor and a pressureless perfect fluid. This modified gravity framework effectively captures different stages of the evolution of the Universe. The reconstructed model is employed to calculate the equation of state parameter, phase planes and the squared speed of sound. The equation of state parameter indicates a quintessence phase, the \(\omega _{\mathbb{D}\mathbb{E}}\)–\(\omega '_{\mathbb{D}\mathbb{E}}\) plane reveals the freezing region and the \(\textbf{r}\)–\(\textbf{s}\) phase plane corresponds to the Chaplygin gas model. Additionally, the squared sound speed parameter suggests instability in the current cosmic evolution. Our study demonstrates that \(f(Q, {\mathbb {T}})\) gravity provides an accurate and comprehensive framework for explaining cosmic expansion, effectively encompassing the dynamics across all stages of the Universe’s evolution.