Emergent universe from Energy–Momentum Squared Gravity

In order to bypass the big bang singularity, we develop an emergent universe scenario within a covariant extension of General Relativity known as \emph{"Energy-Momentum Squared Gravity"}. The extra terms model emerge in high energy regime. Considering dynamics Friedmann-Lema\^itre-Robertson-Walker background, critical points, representing stable Einstein static states phase space, result solutions. It then turns out that equation state parameter $\omega$ gradually declines from constant value $t\rightarrow-\infty$, eventually some past eternal solutions find chance naturally enter into thermal history through graceful exit mechanism. this way, successful realization allows expanding without singularity for spatially flat free cosmological constant.