V/VcO(1),ormin(ijV)cV,|\nabla V| / V \gtrsim c \sim \mathcal{O}(1), \quad \text{or} \quad \min(\nabla_i \nabla_j V) \leq -c' V,
ruling out slow-roll inflation in many setups.
Model Compatibility:
This framework does not require an inflaton or a metastable dS vacuum.
The early universe evolves via quantum tunneling into a structured topological vacuum, with layer-induced expansion mimicking inflation-like effects.
The effective scalar field driving evolution is not fundamental but emergent from layered geometric interaction---bypassing the need for flat scalar potentials.
Thus, the model evades the dS Swampland constraint naturally.
(ii) Distance Conjecture
This conjecture restricts large excursions in moduli space, implying that trans-Planckian field ranges are problematic.
Model Compatibility:
There are no scalar fields with trans-Planckian excursions in this setup.
The effective dynamics are governed by local curvature, tunneling amplitudes, and interlayer phase differences---all geometrically bounded quantities.
Hence, the model is safe under the Distance Conjecture.
(iii) Emergent Geometry and Holography
Recent interpretations of the Swampland criteria suggest that spacetime itself must emerge from quantum information principles, aligning with:
Holographic entropy bounds (as incorporated in our boundary-layer assumptions),
Fractal emergence from RG coarse-graining, consistent with quantum gravity expectations of non-smooth micro-geometries.
By construction, this framework adheres to a bottom-up emergence of geometry and time, further aligning it with Swampland-compatible holographic cosmologies.
