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 of the model emerge in the high energy regime. Considering dynamics in a Friedmann-Lema\^itre-Robertson-Walker background, critical points, representing stable Einstein static states of the phase space, result as solutions. It then turns out that as the equation of state parameter $\omega$ gradually declines from a constant value as $t\rightarrow-\infty$, eventually some of the static past eternal solutions find the chance to naturally enter into thermal history through a graceful exit mechanism. In this way, the successful realization of the emergent universe allows an expanding thermal history without the big bang singularity for the spatially flat universe free of cosmological constant.