A non-singular model universe emerging from scalar-metric cosmology with Chaplygin gas and perfect fluid

While the big-bang singularity has long been considered an unsolved problem in the standard cosmology and inflation theory, new models have been able to find some solutions for it. Here, to avoid the big-bang singularity, we examine the “Emergent Cosmology” scenario as a pre-inflation model, indicating a transition from a past-eternal Einstein static universe (ESU) to the standard inflationary phase. As a model universe, we consider the Sáez and Ballester scalar-metric cosmology comprises a matter part, including the Chaplygin gas and a perfect fluid for which Schutz’s formalism is applied. Employing two methods including the linear stability theory and effective potential approach, we perform a classical analysis of the possible ESUs to discuss the possibility of an Emergent Universe (EU) in a flat, open, and closed Friedmann–Robertson–Walker background. It is found that for any geometry there are some ESUs, among them there is at least one stable ESU that changes to an unstable ESU when the equation of state parameter ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega$$\end{document} for the perfect fluid decreases slowly (or equivalently the cosmic time grows). Therefore, the EU scenario can be realized in the perfect fluid scalar-metric cosmology in the presence of Chaplygin gas for flat, open, and closed universes.