The standard theory of cosmology is based on 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. In 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 is expressed as a parameter known as the cosmological constant. However, initial observations with the Dark Energy Spectroscopic Instrument (DESI) suggest that the speed of comic expansion may vary over time. If further observations confirm this, it could open cosmological models to alternatives to general relativity, known as modified gravity.
In a recent article on arXiv, the authors consider a version of modified gravity known as Horndeski theory. The theory is based on a generalization of general relativity. Einstein's original theory was based on the equivalence principle, from which he derived a generalized description of spacetime in terms of a so-called metric tensor. From this, equations of motion for objects in a gravitational field can be derived, just as Newton's laws lead to equations of motion for objects subjected to physical forces 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 the existence of a uniform scalar field. There are special cases of Horndeski's theory, such as the Brans-Dicke model and the quintessence model. Both models have been used to describe dark energy more generally, including dark matter in some cases. While observations of gravitational waves, galaxy clusters, and cosmic expansion constrain these models to some extent, they do not rule them out entirely. So far, our data on dark energy is not comprehensive enough to distinguish between alternatives.
Comparison between standard model and modified gravity. Photo credit: Chudaykin and Kunz
This latest work examines the DESI results in the context of Horndeski models, and in particular examines how they might account for the temporal evolution of cosmic expansion suggested by the DESI data. It turns out that a modified gravity fits better than the standard model, assuming the time evolution is correct. The study further shows that Horndeski models only work if the temporal evolution of the scalar field correlates with the proposed temporal 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 persists. The Dark Energy Spectroscopic Instrument is still in its early stages and we do not yet know what the final results will be. However, it is clear that Einstein's seat on the theoretical throne is not entirely secure and Horndeski's theory may be the one that steals his crown.
Reference: Chudaykin, Anton and Martin Kunz. “Modified gravity interpretation of evolving dark energy in light of DESI data.” arXiv preprint arXiv:2407.02558 (2024).
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