In this work we discuss the application of the Hamilton-Jacobi formalism on the scalar field implementation of Generalized Chaplygin Gas models. This corresponds to a Generalised Born-Infeld action for the scalar field, which in an initial fast-rolling phase mimics a matter-like behavior and in the final slow-rolling phase mimics a cosmological constant. In order to enrich the phenomenology of the model, we add an extra functional freedom, specified through a scalar potential for the field. Interestingly, we find that, due to the lifting induced by the non-standard kinetic term, an asymptotic de Sitter-like configuration can be obtained even for negative potentials. We show that at the background level, this model can easily mimic the ΛCDM model both with and without independent baryonic and radiation components.

Topological photonic edge states, protected by chiral symmetry, are attractive for guiding wave energy as they can allow for more robust guiding and greater control of light than alternatives; however, for photonics, chiral symmetry is often broken by long-range interactions. We look to overcome this difficulty by exploiting the topology of networks, consisting of voids and narrow connecting channels, formed by the spaces between closely spaced perfect conductors. In the limit of low frequencies and narrow channels, these void–channel systems have a direct mapping to analogous discrete mass–spring systems in an asymptotically rigorous manner and therefore only have short-range interactions. We demonstrate that topological tight-binding models that are protected by chiral symmetries, such as the SSH model and square-root semimetals, are reproduced for these void–channel networks with appropriate boundary conditions. We anticipate, moving forward, that this paper provides a basis from which to explore continuum photonic topological systems, in an asymptotically exact manner, through the lens of a simplified tight-binding model.