The universe sometimes resembles an old fabric: after rapid cooling, wrinkles could have remained — thin, almost invisible threads of monstrous density. They are called cosmic strings. Usually, at the center of such a string hides a singularity — a point where the laws of physics lose their meaning. But the authors of the work took a different variant: a string without a tip, with a smooth profile. It resembles the trace of a ballpoint pen — the pressure is stronger in the middle, weaker toward the edges.
In this toy universe (only two spatial dimensions plus time), they measured the energy that the vacuum accumulates around the string. To do this, they had to gather data on how waves of a scalar field (the simplest kind of matter) scatter on the inhomogeneity of space. The calculation combined two approaches: local — through the Green's function (it shows how a perturbation spreads from a point), and global — through the Jost function (it describes the entire scattering picture as a whole).
Combining the local and global descriptions allowed them to carefully subtract the infinities that always arise in quantum problems. What remained was a finite, physically meaningful addition to the energy — approximately 0.02 in dimensionless units for a specific profile. This is like measuring the tension of an invisible film that wraps around the string.
Such a tool will be useful when physicists want to check whether relic strings leave traces in the microwave background or in gravitational waves. For now, this is pure theory, but each calculated model brings closer the moment when the trace of a pen on the fabric of space can be discerned in real data.
Cosmic strings, if they exist, could be thinner than an atomic nucleus, but a kilometer of such a thread would weigh as much as an entire mountain.