A (Weak) Challenge To Relativistic MOND

MOND is a non-relativistic toy-model modification of Newtonian gravity that accurately models the dynamics of galaxies of all sizes, without dark matter, which was devised by Mordecai Milgrom in 1983. Several attempts have made to generalize the theory relativistically. TeVeS, a tensor-vector-scalar theory (which is also a play on a Hebrew word) by Jacob Bekenstein (who died before his mentor Mr. Milgrom in 2015) was the first notable attempt. RMOND, discussed in the paper below, is another effort to develop a relativistic MOND theory.

The new paper observes that RMOND does not exactly replicate "the expansion history of the Λ cold dark matter (ΛCDM) universe filled solely with dust-like matter," although it can do so with additional degrees of freedom in the matter sector, and is an exact match to the ΛCDM model in the trivial case of a vacuum solution for the evolution of the universe.

In and of itself, this isn't a huge deal. RMOND isn't intended to be identical to the ΛCDM Standard Model of Cosmology. 

For example, one of the generic predictions of MOND cosmologies, and indeed, of essentially any model that replaces dark matter with gravitational effects, is that the progression of galaxy formation in the early history of the universe progresses more quickly. 

Of course, the James Webb Space Telescope has established observationally that galaxy formation in the real universe does not match the predictions of the ΛCDM universe because it occurs too soon (as MOND and other modified gravity theories generically predict). 

Likewise, there are tensions between early measurements of the rate of galaxy expansion as quantified by Hubble's constant, from observations of the cosmic microwave background, and late time measurements of Hubble's constant by other means. Late time measurements of Hubble's constant are significantly larger than the CMB based Hubble constant measurements. 

The EDGES 21cm background radiation measurements also differ dramatically from the ΛCDM model predictions. The EDGES finding has not been replicated yet, however, and there are plausible methodological reasons to question their accuracy.

These observation are examples of data that suggest that there is a real possibility that a simple six parameter ΛCDM model is not an accurate description of the universe. If at least some of the observations contradicting the ΛCDM model cosmology predictions are wrong, then to match what is actually observed, you don't want a theory that exactly matches the expansion history of the ΛCDM model.

But, while the abstract of the new paper doesn't actually say so, the implication is that the ΛCDM model is still a pretty good fit to the expansion history of the real universe, even if it isn't perfect. So, significant deviations from the ΛCDM model which can easily be established without any observations, presents a yellow flag that suggests that RMOND might differ materially from the expansion history of the real universe without further elaboration as well.

In this paper, we present several explicit reconstructions for a novel relativistic theory of modified Newtonian dynamics (RMOND) derived from the background of Friedmann-Lemaı̂tre-Robertson-Walker cosmological evolution. It is shown that the Einstein-Hilbert Lagrangian with a positive cosmological constant is the only Lagrangian capable of accurately replicating the exact expansion history of the Λ cold dark matter (ΛCDM) universe filled solely with dust-like matter and the only way to achieve this expansion history for the RMOND theory is to introduce additional degrees of freedom to the matter sectors. Besides, we find that the ΛCDM-era also can be replicated without any real matter field within the framework of the RMOND theory and the cosmic evolution exhibited by both the power-law and de-Sitter solutions also can be obtained.

Qi-Ming Fu, Meng-Ci He, Tao-Tao Sui, Xin Zhang, "Reconstruction of relativistic modified Newtonian dynamics for various cosmological scenarios" arXiv:2308.00342 (August 1, 2023).