Emergent Cosmology in 4D Einstein Gauss Bonnet Theory of Gravity

In this paper, in an FLRW background and a perfect fluid equation of state, we explore the possibility of the realization of an emergent scenario in a 4D regularized extension of Einstein-Gauss-Bonnet gravity, with the field equations particularly expressed in terms of scalar-tensor degrees of freedom. By assuming non-zero spatial curvature ($k = \pm 1$), the stability of the Einstein static universe (ESU) and its subsequent exit into the standard inflationary system is tested through different approaches. In terms of dynamical systems, a spatially closed universe rather than an open universe shows appealing behaviour to exhibit a graceful transition from the Einstein static universe to standard cosmological history. We found that under linear homogeneous perturbations, for some constraints imposed on the model parameters, the Einstein static universe is stable under those perturbations. Moreover, it is noted that for a successful graceful transition, the equation of state $\omega$ must satisfy the conditions $-1 < \omega <0$ and $\omega < -1$ for closed and open universes, respectively. Also, under density perturbations, the Einstein static universe is unstable if the fluid satisfies the strong energy condition but is stable if it violates it, for both closed and open universes. Furthermore, the Einstein static universe is seen to be stable under vector perturbations and tensor perturbations, regardless of whether the fluid obeys or violates the SEC.