A new study has calculated the vacuum polarization energy (VPE) for a scalar field in the background of a nonsingular cosmic string in 2+1 spacetime dimensions. This work is significant because it addresses VPE in a cosmic string model with a finite radius, unlike idealized infinitely thin string models. VPE is a manifestation of the zero-point energy of quantum fields, which is modified by spacetime geometry, and its precise calculation is crucial for understanding how quantum effects manifest in the vicinity of exotic astrophysical objects like cosmic strings.

The calculation expresses the VPE as a renormalized sum and integral over scattering data. For the "ballpoint pen" model (analogous to a square well in curvature), these data can be expressed in terms of Legendre and Bessel functions. For more generic string profiles, the results are obtained numerically. The study also explores how relationships between the local density of states (expressed via the Green's function) and the global density of states (via the Jost function) extend to this curved spacetime background, allowing for precise implementation of perturbative renormalization conditions.

This advance is relevant for theoretical physics and cosmology, as cosmic strings, though hypothetical, are predicted by some grand unified theories and might have played a role in the early universe. Understanding VPE in their proximity could offer clues about their physical properties and potential detectability. Furthermore, the methodology developed for renormalization in this curved spacetime context could be applicable to other problems where the interaction between quantum fields and non-trivial geometries is fundamental.