Dark matter is a central but contentious part of the dominant model of cosmology. It has never been observed directly and is seen as an arbitrary add-on to Einstein's theory of gravity, just to make the data fit. MOND has for a long time been considered the most credible alternative theory of gravity, doing away with the need to postulate dark matter. But a recent study lead by Dr Indranil Banik, a past supporter of MOND, demonstrates that the theory is in fact wrong. The search for a more credible alternative continues.
According to the dominant paradigm in cosmology, the majority of the stuff that makes up our universe is not the ordinary matter we see around us, but something called dark matter. According to this standard model of cosmology, dark matter has a gravitational effect at large scales in the universe, effects that are not observable at smaller scales like our Solar System. The only problem is, no one has ever observed dark matter directly – its existence is only postulated by its supposed gravitational effect at large scales. I have been a critic of the dark matter hypothesis, and in the past have expressed an interest in its main alternative –Milgromian dynamics, or MOND for short. MOND has been heralded as making better sense of the data astronomers gather, and as having made accurate predictions, whereas dark matter theory has to retrospectively adjust to make sense of new data. But according to a recent paper I published along with colleagues, I show that MOND is in fact wrong. That leaves cosmology without an accurate or complete theory of gravity, opening up the prospect for a paradigm shift in our understanding of gravity.
One of the big mysteries in astrophysics today that has dark matter theorists clash with MOND supporters concerns the rotation speed of stars and gas in galaxies. As you go further from their centre, the rotation speed remains almost the same, even when you are far beyond the extent of the visible matter. These flat rotation curves are unlike the Solar System, where more distant planets orbit the Sun more slowly (in addition to facing a larger orbit). Scientists are unsure of how to solve this missing gravity problem in galaxies, but one leading idea is to add a halo of dark matter around each one, supposedly adding a gravitational pull. This solution, of course, is very speculative because nobody has ever seen the dark matter other than indirectly through the gravity it creates, making it plausible that the problem instead lies with our understanding of gravity.
This is where MOND comes in as a potential alternative model of gravity. According to MOND, the gravitational field from a point mass declines according to the Newtonian inverse square law of gravity that we are all familiar with only when the strength of gravity is above a threshold called a0. Within this Newtonian regime, gravity becomes 4 times weaker at double the distance. Once gravity becomes weaker than a0, MOND postulates that gravity switches to an inverse distance decline, so it still weakens with distance – but now doubling the distance halves the gravity in the MOND regime.
Because MOND operates at low accelerations rather than beyond a fixed length, wide binary stars are perfect for testing out the theory.
This threshold a0 is about 2500 times weaker than the gravity on our most distant spacecraft, so we have no experience of how gravity behaves when it is that weak. Assuming a smooth transition between the Newtonian and MOND regimes, it is possible to make sense of the rotation curves of a huge diversity of galaxies using only their visible mass, without needing to postulate any dark matter. MOND accurately predicts even the gravitational lensing effect of background objects by galaxies, which can be measured from subtle distortions to the apparent shapes of background galaxies as the foreground galaxy bends the light coming from them.
Because MOND operates at low accelerations rather than beyond a fixed length, wide binary stars – binary stars with a separation of a few thousand astronomical units such that the gravity between them is around a0 or weaker – are perfect for testing out the theory. Local wide binaries are subject to the external gravity from the rest of the Galaxy. Taking this into account, wide binaries should orbit each other 20% faster than the Newtonian prediction if MOND is correct. Wide binaries would be barely affected by dark matter because of their size – they are much smaller than galaxies and so contain negligible amounts of dark matter (if any). This all means that accurate observations of a large number of wide binaries promise to put clear water between Newtonian and Milgromian gravity.
I have been working towards this wide binary test (WBT) for over six years and on MOND more broadly for just over a decade. Given the importance of the WBT, I posted a detailed plan of how to implement it so that I would not be tempted to alter the analysis to change the result. As a theorist, I consulted expert observers at Queen Mary University of London and elsewhere on how best to do the test, which fed into the plan. Building on this plan, I led an international team to conduct the WBT using data from the European Space Agency’s Gaia mission, which launched in December 2013, providing very precise positions of stars over several years.
The results of our research decisively reject MOND in a wide range of ways of looking at the data.
The results of our research decisively reject MOND in a wide range of ways of looking at the data, some simple and others more complicated, some involving more plausible assumptions and others involving somewhat less plausible assumptions. The paper also explains in detail why recent claims that the WBT in fact confirms MOND were wrong. In short, there was no good quality cut on the uncertainty in the relative velocity of the stars in each wide binary This is something that I handled extremely carefully because such uncertainties are not directly included in the analysis – I instead relied on data for only those systems where the uncertainty is very small. I was also careful to discuss a wide range of possible confounding factors and why these are unlikely to have made a Milgromian population of wide binaries look Newtonian. This would require a very precise cancellation of the predicted MOND effect in a way that has to be considered extremely dubious.
Aside from the movement of binary stars, MOND also predicts subtle deviations to the orbits of planets in the Solar System. While the effect is much smaller than the 20% signal in wide binaries, we have much more precise data from spacecraft. As a result of the Cassini mission to orbit Saturn, there is a tight upper limit on a parameter which quantifies how big any non-Newtonian forces can be. It has recently become clear that given rotation curve constraints on MOND, it predicts a value for the relevant parameter 9 times larger than observed. Combined with the WBT, this implies MOND just does not work on scales below about a light year.
MOND also encounters severe difficulties when applied to scales larger than a single galaxy, for example galaxy clusters, as shown in the figure below.
This plot shows radial acceleration data taken from disc galaxies (grey) and galaxy clusters (black with error bars), with y-axis representing the observed gravitational acceleration and the x-axis representing Newtonian gravity’s prediction. The solid red line represents MOND’s prediction which, once uncertainties are considered, fits the disc galaxy data. However, when looking at the scale of galaxy clusters, the data closely follow the upper dotted line which is the expected relation in ΛCDM paradigm if the universe has 5 times as much dark matter as normal matter. Credit: Adapted by Pengfei Li from figure 5 of Li+ 2023.
The difficulties encountered by MOND on scales smaller and larger than the galaxy scales for which it was designed imply that MOND is not a fundamental theory. However, the standard cosmological model, known as ΛCDM – which predicts the existence of dark matter – faces its own challenges. I have come to the conclusion that Einstein’s theory of gravity (General Relativity) – which we know reduces to Newtonian gravity in galaxies and wide binaries – does not require substantial modifications on scales of up to several million light years. But deviations are likely on much larger scales. This would help to explain why we appear to be in a huge void which is about 20% less dense than the average for the Universe as a whole out to a distance of a billion light years. Such a void can help to solve the Hubble and bulk flow tensions for ΛCDM. While these are all very serious tensions, the Hubble tension in particular has garnered a lot of attention because it relates to the present expansion rate of the Universe or the Hubble constant, one of the most basic cosmological parameters. Local measurements indicate that this is 10% higher than predicted based on observations of the early Universe if we use the ΛCDM framework. Since observations also indicate that we are in a large and deep void, it would be natural if the Hubble tension is caused by matter flowing out of the void due to the gravitational pull from the higher density of matter outside the void. This would inflate the locally measured Hubble constant. It would also naturally account for the average velocity of galaxies out to a billion light years, an observation known as the bulk flow – which is about twice as fast as expected in ΛCDM.
Therefore, it is still quite likely that there are modifications to be made to Einstein’s General Relativity theory. However, this would be on scales of tens to hundreds of millions of light years, not on the scales of individual galaxies or galaxy clusters. Such a modification may possibly have enhanced the formation of the most massive galaxy clusters. But it would leave unanswered the issue of why galaxies follow MOND so closely. This is not easily understood in the ΛCDM paradigm.
As long as dark matter is not directly detected, we should keep an open mind to any completely new ideas about cosmology, though we must also be willing to discard such ideas if they encounter any major inconsistencies with observations.
But at the same time, there are many aspects of cosmology which the ΛCDM paradigm does explain very well, ranging from the mass distribution of galaxy clusters in the local Universe to the abundances of deuterium and helium made in nuclear reactions in the first few minutes after the Big Bang. Science does not work by pointing out the successes of a model and arguing that it is unlikely for any other explanation to also work. Prior predictions are a part of science, but really scientists should be trying to falsify their theories. Correct predictions do not confirm a theory, but a clear falsification means we can be sure that it is wrong, at least as presently formulated. This is definitely the case for MOND, which completely fails when tested on even slightly smaller or larger scales than those for which it was designed. ΛCDM also fails, but it can be extended much further from the infant Universe where its parameters are usually calibrated. This means it likely provides a better starting point for building a more complete picture of the Universe.I think the best approach is to modify it further by changing the law of gravity on very large scales and changing the properties of dark matter to better account for the behaviour of galaxies. But as long as dark matter is not directly detected, we should keep an open mind to any completely new ideas about cosmology, though we must also be willing to discard such ideas if they encounter any major inconsistencies with observations.
Credit: Adapted by Pengfei Li from figure 5 of Li+ 2023 (LINK TO https://arxiv.org/abs/2303.10175).