Supernovae Constraints on Cosmological Density Parameter and Cosmic Topology

We illustrate the constraints that a possible detection of a non-trivial spatial topology may place on the cosmological density parameters by considering the $\mathrm{\Lambda }$CDM model Poincar'e dodecahedal space (PDS) topology as a circles-in-the-sky detectable topology. To this end we reanalyze the type Ia supernovae constraints on the density parameter plane ${\mathrm{\Omega }}_k$–${\mathrm{\Omega }}_{\mathrm{\Lambda }}$ and show that a circles-in-the-sky detectable PDS topology gives rise to important constraints on this parameters plane.