Stability of the Einstein static universe in Eddington-inspired Born-Infeld theory

By considering the realization of the emergent universe scenario in Eddington-inspired Born-Infeld (EiBI) theory, we study the stability of the Einstein static universe filled with perfect fluid in EiBI theory against both the homogeneous and inhomogeneous scalar perturbations in this work. We find that in both the spatially flat and closed cases, the emergent universe scenario is no longer viable, since the Einstein static universe cannot be stable against both the homogeneous and inhomogeneous scalar perturbations simultaneously. However, the emergent universe scenario survives in the spatially open case, while the Einstein static universe can be stable under some conditions.

Figure 1

The stable regions with $Z>0$ for the case of the spatially closed universe ($K=+1$). The red dashed lines and the black solid lines are the contours with $Z=0$ for the homogeneous ($k^2=0$) and inhomogeneous ($k^2=n(n+2)\ge 8$) scalar perturbations, respectively. See the text for details.

Figure 2

The stable regions with $Z>0$ for the case of the spatially open universe ($K=-1$). The red dashed line and the black solid line are the contours with $Z=0$ for the homogeneous ($k^2=1$) and inhomogeneous ($k^2=n^2+1>1$) scalar perturbations, respectively. See the text for details.