Cosmologically Viable Solutions in Geometric Modified Gravity

The discovery of the accelerated expansion of the universe highlighted General Relativity's inability to naturally account for dark energy without invoking a finely tuned cosmological constant. In response, a wide range of alternative paradigms have been proposed. Among these, Teleparallel Gravity and Symmetric Teleparallel Gravity, which depart from the Riemannian framework of General Relativity and instead rely on torsion or non-metricity to describe gravitational interactions, have gained increasing attention in recent years. We explore extensions of these non-Riemannian approaches, aiming to replicate the observed late-time acceleration of the universe by emulating the cosmological constant's role. We also evaluate the consistency of these theories with local gravity constraints by studying their static, spherically symmetric solutions. We show that although some models can reproduce the desired cosmological behavior, they often fail to meet Solar System observational bounds, particularly through deviations in the predicted Eddington parameter. Our findings underscore the need for a unified approach that tests modified gravity theories across both cosmological and local scales.