Stability of the Einstein Static Universe in Zero-Point Length Cosmology with Topological Defects

Abstract: Recently, zero-point length cosmology has shown some positive insights into some non-singular aspects of the early Universe. In addition, topological defects are known to play a significant role by its presence as a part of the total energy in the very early Universe. We investigate the stability issue of the Einstein static phase in the emergent scenario of the Universe in a generalized framework of zero-point length cosmology in the presence of topological defects in the very early times. We derive the modified Friedmann equations, where the matter sector includes an extra energy density term arising from $n$-dimensional topological defects. We have studied the possibility of graceful exit of emergent scenario and its stability using dynamical system analysis and against homogeneous scalar perturbation. We also analysed the stability against inhomogeneous density perturbation, vector perturbation and tensor perturbation. Through the stability analysis, it has been shown that the model parameters associated with zero-point length setting and $n$-dimensional topological defects play a visible role in the phase transition process from the ESU to the inflationary regime. Also, interestingly it is found that there exists a mutual interplay between the zero-point length parameter, and the dimension of topological defect on the stability of the ESU on the basis of inhomogeneous density perturbation. Finally, the stability is also tested against vector and tensor perturbation, which shows that the ESU is stable against such perturbations.