Abstract
The works reported in this thesis primarily address the application of the Raychaudhuri equation in two intriguing problems in gravitational physics. These problems still lack universally accepted explanations. The first problem is related to the existence of spacetime singularities. We aim to find possible escape routes from these problematic singularities at the classical level. The second problem is associated with the late time accelerated expansion of the Universe. In this context, our goal is to find a possible explanation of this phenomenon without assuming the presence of any exotic contribution to the stress-energy tensor.
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