“…Many authors have studied the stability of cosmological models using various techniques, some of them are Nimkar et al [24], Geovanny et al [25], Katore et al [26,27], Shah et al [28], Ahmed et al [29], Sharif et al [30], Knutsen [31,32], and Wanas et al [33], Vinutha et al [34], Koussour et al [35], Yadav et al [36], Chiang-Mei Chen et al [37], and Saha et al [38]. Also, Santhi et al [39], Thakur [40], Zhai et al [41], and Debnath et al [42] proposed a new parameter called the ( diagnostic. Drawing inspiration from the previously mentioned works, this research investigates an axially symmetric cosmological model with perfect fluid in the presence of Lyra geometry.…”