The Effects of Spatial Curvature on Cosmic Evolution

As evidenced by a great number of works, it is common practice to assume that the Universe is flat. However, the majority of studies which make use of observational data to constrain the curvature density parameter are premised on the $\Lambda$CDM cosmology, or extensions thereof. On the other hand, fitting the data to models with a time-varying dark energy equation of state can, in some cases, accommodate a non-flat Universe. Several authors caution that if the assumption of spatial flatness is wrong, it could veer any efforts to construct a dark energy model completely off course, even if the curvature is in reality very small. We thus consider a number of alternative dynamical dark energy models that represent the complete cosmological scenario, and investigate the effects of spatial curvature on the evolution. We find that for a closed Universe, the transition to the epoch of decelerated expansion would be delayed with respect to the flat case. So would the start of the current dark energy-dominated era. This would be accompanied by a larger inflationary acceleration, as well as a larger subsequent deceleration. The opposite behavior is observed if the Universe is open.