In one hospital ward it's +40°C, in another +10°C, and on average it's +25°C. If temperature affected something nonlinearly (say, the rate of bacterial growth) the average would give a wrong prediction. The same problem arises when cosmologists describe a universe where galaxies are packed into clusters and voids yawn between them.
Most calculations of cosmic expansion use 'uniform dust'—matter evenly smeared across space. It's convenient, but reality is different: matter is clumped. In standard gravity (general relativity), this substitution usually works because the coupling between gravity and matter is linear. But if gravity depends on matter nonlinearly (as in some extended theories, for instance when a function of the trace of the energy–momentum tensor is added to the equations) then averaging is no longer harmless.
The authors took a simple model — global monopoles, hypothetical point-like defects in space that could have formed in the early universe. They showed that if you average a nonlinear function of density over a volume and then plug in the average density, the result won't match what you get by first plugging in the real matter distribution and then averaging. The difference depends on how many particles are in a unit volume. For dust (ordinary pressureless matter), such theories give rise to a nonzero pressure, even though in standard cosmology dust has no pressure.
This means that in models with nonstandard gravity–matter coupling, you cannot ignore the universe's inhomogeneity. Otherwise, predictions about how fast the cosmos expands will be wrong. The universe is not just 'on average' homogeneous: its lumpiness can affect the most global processes.
as written by the authors arXiv:2602.15448
We address the challenge, commonly referred to as the cosmological averaging problem, of relating the large-scale evolution of an inhomogeneous universe to that predicted by a homogeneous matter distribution in theories of gravity with nonminimal matter-gravity couplings. To this end, we focus on the class of $$f(R,T)$$ models given by $$f(R,T) = R + F(T)$$, where $$R$$ denotes the Ricci scalar and $$T$$ the trace of the energy-momentum tensor. This framework provides a simple yet theoretically consistent realization of nonminimal coupled gravity and can be recast as General Relativity minimally coupled to a modified matter Lagrangian. Using global K-monopoles as an illustrative toy model, we show that, when $$F$$ is a nonlinear function of $$T$$, the ratio between the spatial average of $$F$$ and $$F$$ evaluated at the spatial average of $$T$$ can deviate significantly from unity and depends on the particle number density. We demonstrate that the common assumption that this ratio is equal to unity generally leads to an inaccurate description of cosmological dynamics. We further show that dust in these theories generally exhibits a non-vanishing proper pressure. Our results highlight the importance of properly accounting for spatial averaging in cosmological models with nonminimal matter-gravity couplings.
Global monopoles are hypothetical objects that could have formed during phase transitions in the early universe, much like defects in a crystal lattice when water freezes. They haven't been detected yet, but they serve as a handy 'toy' for testing theories of gravity.
In Greg Egan's novel Schild's Ladder, physicists confront the possibility that the vacuum might be unstable due to exotic fields — a similar concern echoes in theories with nonstandard gravity, where 'empty' space might behave unexpectedly.