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

To seek for a singularity free model universe from a perfect fluid scalar-metric cosmology, we work in the “Emergent Cosmology” (EC) paradigm which is a non-singular alternative for cosmological inflation. By using two methods including Linear Stability Theory and Effective Potential Formalism, we perform a classical analysis on the possible static solutions (that are called usually as Einstein Static Universes (ESU)in literature) in order to study EC paradigm in a FRW background. Our model contains a kinetic term of the scalar field minimally coupled to the background geometry without a potential term. The matter content of the model consists of a perfect fluid plus a cosmological constant (Lambda ) as a separate source. In the framework of a local dynamical system analysis, we show that in the absence or presence of (Lambda ), depending on some adopted values for the free parameters of the underlying cosmological model with flat and non-flat spatial geometries, one gets some static solutions which are viable under classical linear perturbations. By extending our study to a global dynamical system analysis, we show that in the presence of (Lambda ) with non-flat spatial geometries there is a future global de Sitter attractor in this model. Following the second method, we derive a new static solution that represents a stable ESU but this time without dependence on the free parameters of the cosmological model at hand. As a whole, our analysis suggests the possibility of graceful realization of a non-singular EC paradigm (i.e. leaving the initial static phase and entering the inflation period as the universe is evolving) through either preserving or violation of the strong energy condition.