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To seek for a singularity free model universe from a perfect fluidscalar-metric cosmology, we work in the "\emph{Emergent Cosmology}" (EC)paradigm which is a non-singular alternative for cosmological inflation. Byusing two methods including Linear Stability Theory and Effective PotentialFormalism, we perform a classical analysis on the possible static solutions(that are called usually as Einstein Static Universes (ESU)in literature) inorder to study EC paradigm in a FRW background. Our model contains a kineticterm of the scalar field minimally coupled to the background geometry without apotential term. The matter content of the model consists of a perfect fluidplus a cosmological constant $\Lambda$ as a separate source. In the frameworkof a local dynamical system analysis, we show that in the absence or presenceof $\Lambda$, depending on some adopted values for the free parameters of theunderlying cosmological model with flat and non-flat spatial geometries, onegets some static solutions which are viable under classical linearperturbations. By extending our study to a global dynamical system analysis, weshow that in the presence of $\Lambda$ with non-flat spatial geometries thereis a future global de Sitter attractor in this model. Following the secondmethod, we derive a new static solution that represents a stable ESU but thistime without dependence on the free parameters of the cosmological model athand. As a whole, our analysis suggests the possibility of graceful realizationof a non-singular EC paradigm (i.e. leaving the initial static phase andentering the inflation period as the universe is evolving) through eitherpreserving or violation of the strong energy condition.

Non-singular model universe from a perfect fluid scalar-metric cosmology