From René Thom to the Cosmos: Universal Singularities in Collapsing Domain Walls
by
IFAE Seminar Room
In-person
Domain walls—topological defects born from primordial symmetry breaking—are fundamental to early-universe cosmology. Understanding their collapse is crucial for constraining inflationary and beyond-Standard-Model scenarios.
While large-scale network simulations remain essential and computationally expensive, we adopt a complementary approach: studying individual closed walls through analytical, approximate, and numerical methods.
Our key finding: collapsing domain walls generically develop universal singularities—cuspidal edges and vertices that propagate at the speed of light. Remarkably, their dynamics follow the mathematical patterns predicted by René Thom's theory, as shown by full-field-theory adaptive-mesh-refinement simulations. Remarkably, their dynamics follow the mathematical patterns predicted by René Thom's Catastrophe Theory.
By connecting Singularity Theory, Eikonal caustics, and relativistic field dynamics, we reveal deep universality: the same mathematics governing optical caustics, wavefront formations, and—as Salvador Dalí intuited—artistic geometry.
Dorian Amaral, Elia Bertoldo, Tomas Kvietkauskas, Clarisse Prat, Francesco Sciotti