Non-singular flat universes in braneworld and loop quantum cosmology

In this paper we consider an exotic matter source with nonlinear Equation of state and a minimally coupled scalar field with two different potentials that produce a closed inflationary emergent universe in the relativistic context. We study all these three cases both in the context of Randall–Sundrum braneworld and effective Loop quantum cosmology (LQC) for vanishing spatial curvature that is observationally favored and in the absence of any effective cosmological constant term. We solve the modified Friedmann equations in each case to obtain the time evolution of the scale factor and use it to check whether the initial singularity can be averted. In almost all the cases we find the initial singularity is absent. We study the nature of the slow-roll inflation in the cases where we obtain inflationary emergent universes. The inflationary scenario is found to be improved than in a standard relativistic context and we compare the improved scenario for both the braneworld and LQC models. Interestingly, we also obtain bouncing and cyclic universes from our analysis in some cases. The initial singularity can be averted with the matter EoS or scalar field potential respecting the Null Energy condition, taking into account effective high energy (curvature) corrections with or without extra dimensions. The UV corrected scenario allows a spatially flat universe to behave effectively like a closed one and the initial singularity can be avoided by suitable bounce or emergence mechanisms as obtained.