Abstract
Nontrivial spacetime configurations emerge naturally across gravitational and cosmological regimes, providing new links between departures from standard geometric frameworks and observable phenomena. In this thesis we begin by examining a topologicaldrive metric in the classical general relativity setting: a bubble-universe detachment and reconnection mechanism that reveals how exotic matter and quasiregular singularities accompany nontrivial structures in spacetime. We then turn to the early-universe epoch, employing lattice simulations of multi-stream inflation to trace how gradient energy, potential barrier structure, and field fluctuations govern bifurcation probability and the geometry of bubble-like domains. These domains may evolve into large-scale structure inhomogeneities such as gigaparsec-scale voids. Focusing next on the late universe, we investigate observational signatures of such void models and show how an off-centre observer embedded in one may experience altered dipolar anisotropies, thereby offering insight into the cosmic dipole anomalies. We further explore wormhole-lensing, deriving weak-field deflection-angle corrections up to the order of 1/b4 that demonstrate how wormholes might ultimately be distinguished from black holes in future lensing observations. Taken together, these studies investigate nontrivial spacetime configurations in multiple physical regimes and identify the dynamical and observational signatures they may produce. This thesis broadens the range of viable spacetime structures and maps their potential signatures beyond the standard cosmological paradigm.