A scale that weighs not a body, but the very space around it. That's how Einstein's equations work in general relativity: they link the curvature of spacetime to what resides within it. On the right-hand side, the "matter" side, you typically plug in either energy density or pressure. For the classical theory, it doesn't matter: you get the same answer either way.
But when physicists build new gravity models (say, to explain dark energy or dark matter) this innocent substitution stops working. The equations start to depend on your choice, as if the scale suddenly gave different readings depending on which side you look at it from. The reason is that such models introduce second derivatives of the matter Lagrangian with respect to the metric — the tensor describing geometry. The Lagrangian isn't just energy; it's the difference between kinetic and potential energy. For a perfect fluid, it's expressed precisely through density or pressure. If you treat the particle velocity and the geometry as independent, confusion arises.
The authors of the new work propose a way out: stop treating the four-velocity and the metric as independent. Then the ambiguity vanishes, and modified gravity becomes "honest"—its predictions no longer depend on what we plug into the right-hand side. They tested their approach on two extremes: in the ultra-dense cores of neutron stars (where pressure is enormous) and in the early Universe filled with radiation (where pressure is one-third of energy density). A neutron star is the collapsed core of a supernova explosion. A teaspoon of its material weighs as much as a mountain. In both cases, the method clarifies which option is correct.
So the scale for spacetime finally gets an unambiguous instruction: what exactly to place on the "matter" pan. This isn't just a technical tweak; it's a step toward a clearer understanding of how matter bends space in the most extreme corners of the cosmos.
In a neutron star, the pressure at the center can reach $10^{34}$ pascals: that's like a billion billion Earth atmospheres pressing on every square meter.