Modified Energy,
Modified Gravity

J. M. Ezquiaga and M. Zumalacárregui (2018)

The standard theory of cosmology is based upon four things: the structure of space and time, matter, dark matter, and dark energy. Of these, dark energy is the one we currently understand the least. Within the standard model, dark energy is part of the structure of space and time as described by general relativity. It is uniform throughout the cosmos and expressed as a parameter known as the cosmological constant. But initial observations from the Dark Energy Spectroscopic Instrument (DESI) suggest the rate of comic expansion may vary over time. If further observations reinforce this, it could open up cosmological models to alternatives to general relativity known as modified gravity.¹

In a recent paper on the arXiv, the authors look at one version of modified gravity known as Horndeski’s theory. The theory is based upon a generalization of general relativity. Einstein’s original theory was based upon the principle of equivalence, from which he derived a generalized description of spacetime through what is known as a metric tensor. From this, you can derive the equations of motion for objects in a gravitation field, just as Newton’s laws lead to equations of motion for objects under physical and gravitational forces.

General relativity is the simplest model with a metric tensor. Horndeski’s theory is the most general model with a metric tensor and allows for the presence of a uniform scalar field. There are special cases of Horndeski’s theory, such as the Brans-Dicke model and the model of quintessence. Both of these models have been used to describe dark energy in a more general way, as well as dark matter in some cases. While observations of gravitational waves, galactic clustering and cosmic expansion constrain these models to some degree, they don’t entirely rule them out. So far, our data on dark energy isn’t rich enough to distinguish between alternatives.

Chudaykin and Kunz

This latest work looks at the DESI results in the context of Horndeski models, specifically looking at how it might address the time-evolution of cosmic expansion suggested by the DESI data. It found that if the time evolution is taken to be correct, then a modified gravity is a better fit than the standard model. The study goes on to show that Horndeski models only work where the time evolution of the scalar field correlates to the proposed time evolution of dark matter. This rules out some Horndeski models that have been used to explain dark matter.

Overall, the authors argue that the DESI observations make Horndeski’s theory a viable alternative to general relativity. That is, if the data holds up. The Dark Energy Spectroscopic Instrument is still in its early stages, and we don’t yet know what the final results will be. But it is clear that Einstein’s seat on the theoretical throne isn’t entirely assured, and Horndeski’s theory might just be the one to steal the crown.