Non-Geometric Compactifications and String Cosmology in the Swampland

This thesis comprises three research projects conducted during the author's doctoral program, which are presented individually in the following chapters. In Chapter II, we demonstrate that field trajectories leading to cosmic acceleration and exhibiting rapid turns near the boundary of the moduli space lie within the Swampland. Specifically, our analysis assumes the validity of the Swampland Distance Conjecture in the presence of a scalar potential and focuses on hyperbolic spaces, as prototypical geometries characterizing infinite distance limits in Calabi--Yau compactifications. We find that, in a quasi-de Sitter space with Hubble rate $H$ and acceleration parameter $\epsilon$, the turning rate $\Omega$ is subject to an upper bound, $\Omega/H\lesssim\mathcal{O}(\sqrt{\epsilon})$. Therefore, field trajectories consistent with the SDC can only have a negligible deviation from geodesics. This places strong constraints on the viability and consistency of multi-field quintessence scenarios in string theory. Within this framework, we further show that for a universe with asymptotic accelerated expansion, the asymptotic de Sitter conjecture is generically violated. Chapter III investigates the feasibility of a classical realization of the Dark Dimension Scenario through T-fold compactifications on $T^5 \times S^1$. The Dark Dimension Scenario posits the existence of a single extra dimension in our Universe, which is mesoscopically large and may be accessible to near-future experimental probes. By utilizing Scherk-Schwarz reduction from 5D to 4D and incorporating duality twists via T-fold fluxes associated with $T^5$, we achieve stabilization of the $T^5$ volume modulus as well as several other geometric moduli. This construction generates a scalar potential exhibiting two runaway directions, one of which is aligned with the Scherk-Schwarz radion corresponding to the $S^1$. Upon further stabilization, we find that this $S^1$ naturally realizes the mesoscopic extra dimension required by the Dark Dimension Scenario, as the resulting effective potential scales as $V \sim m_{\text{KK}}^4$, in agreement with the expectations of the scenario. In Chapter IV, we employ freely acting asymmetric orbifolds of type IIB string theory to construct a class of four-dimensional theories with eight supercharges. The resulting low-energy effective theories are analogous to $STU$ models, but with a key distinction: the free orbifold action reduces the duality group to a congruence subgroup of the parent toroidal compactification. This reduction enlarges the moduli space, introducing both singular loci at finite distance and additional infinite distance limits. We verify that the Swampland Distance Conjecture and the Emergent String Conjecture are satisfied in the non-geometric compactifications of string theory considered here. In particular, we identify infinite distance points in the moduli space at which the theory decompactifies to distinct higher-dimensional compactifications.