Dark Matter And Dark Energy As Emergent Gravity Recalled

A paper published in a Korean physics journal this year, which has its roots in a five year old preprint and a four year old conference paper, looks at the possibility of explaining dark matter and dark energy in an emergent gravity theory.

The gist of the paper is the time-like quantum vacuum fluctuations from Standard Model forces can give rise to an attractive force that might explain dark matter, while space-like quantum vacuum fluctuations from the Standard Model forces can give rise to a repulsive force that might explain dark energy, as the three parts space-like fluctuations to one part time-like fluctuations mirror the cosmological estimates of the relative magnitude of dark matter and dark energy in the observable universe.

It is more whimsy than a solid effort to see if this concept would really work at the level that other explanations of dark matter and dark energy have been examined. It doesn't apply the concept to specific galaxies or otherwise make sure that the distribution of the effects matches astronomy observations.

But the concept of gravity or some gravitational phenomena arising emergently as a residual effect of Standard Model interactions, most notably advanced by Erik Verlinde in a more testable and close to viable model, is appealing. Reducing four core theory forces to three at a fundamental level would be a great accomplishment for reductionist physics. Wikipedia, at the link above, sums up Verlinde's emergent gravity theory as follows:

On 8 November 2016 Erik Verlinde published his new theory of gravity, where gravity is not one of the four fundamental forces of physics but, rather, gravity is emergent from other fundamental forces. In this work, he argues that unlike in anti-de Sitter (AdS) space, holography and the area law do not apply exactly in de Sitter space (which models our universe) because there is an additional entropy associated with the cosmological horizon. If this entropy were evenly distributed throughout space, it would contribute a volume law term to the entropy which becomes dominant at large length scales and is related to dark energy. He further argues that this entropy modifies emergent gravity, introducing residual forces when the acceleration due to gravity is very weak.  

The result provides a candidate explanation for dark matter similar to the Modified Newtonian Dynamics (MOND) proposal and explains the empirical relationship between dark matter and the Hubble constant. By Aug 1st 2018 the paper has been quoted in 153 physics papers, including by well-known physicists such as Lee Smolin, and Mordehai Milgrom - originator of MOND. Explanation of modified gravity through entropic gravity is a "quantum gravity theory" merging "general theory of relativity" with "quantum field theory". Verlinde himself names it also quantum information theory. 

There are already critical papers on "emergent gravity" such as "Inconsistencies in Verlinde’s emergent gravity" by D Dai, D Stojkovic (Springer HEP, Nov 2017), stating that "...When properly done, Verlinde’s elaborate procedure recovers the standard Newtonian gravity instead of MOND".

The criticisms of emergent gravity are serious, but subsequent papers by Verlinde and other physicists who have continued to work on this theory suggest that these criticisms may not be an insurmountable.

The Korean emergent gravity paper published this year, but written hot in the wake of Verline's emergent gravity paper, and its abstract are as follows: 

Emergent gravity can be applied to a large N matrix model by considering the vacuum of a noncommutative (NC) Coulomb branch that satisfies the Heisenberg algebra. Due to the fact that IR fluctuations in the NC Coulomb branch always pair with UV fluctuations, this UV/IR mixing is extendable to a macroscopic scale. These vacuum fluctuations in the NC Coulomb branch are described by a four-dimensional NC U(1) gauge theory. The order parameter for the vacuum fluctuations is given by random four-vectors that have their own causal structure in the commutative limit unlike the conventional cosmological models based on a scalar field theory coupled to gravity. 

We show that their causal structure results in the different nature of gravitational interactions so that space-like fluctuations give rise to the repulsive gravitational force while time-like fluctuations generate the attractive gravitational force. Given the fact that the fluctuations are random in nature and we live in a (3+1)-dimensional spacetime, the ratio of the repulsive vs. attractive components ends up being 3:1 = 75:25, which is interestingly consistent with the dark components of the current universe. If we include ordinary matters acting as an attractive gravitational force, the emergent gravity could more accurately explain the dark side of our universe. 

This work is an expanded version of the conference proceedings (Yang in EPJ Web Conf 168:03006, 2018).

Jungjai Lee, Hyun Seok Yang, "Dark Energy and Dark Matter in Emergent Gravity" arXiv:1709.04914 (September 14, 2017, last revised November 1, 2022 )and 81(9) Journal of the Korean Physical Society 910-920 (2022).