The universe is observed to be in an accelerated expansion phase, a phenomenon conventionally attributed to the presence of Dark Energy within the \(\Lambda CDM\) cosmological model. However, the elusive nature of this dark component and the theoretical challenges it presents motivate the exploration of alternative interpretations. In this review, we describe two recent theoretical frameworks, of our research group, that aim to account for cosmic acceleration without invoking dark energy. Specifically, we examine a model based on hyperbolic motion in cosmological spacetime and another that modifies the time-redshift relation. We demonstrate how these approaches successfully mimic current experimental observations, such as Type Ia supernovae luminosity distances, offering compelling alternatives to the standard cosmological constant paradigm.
