According to Sir Isaac Newton’s theory of Universal Gravitation, gravity is an action at a distance, where one object feels the influence of another regardless of distance. This became a central feature of Classical Newtonian Physics that remained the accepted canon for over two hundred years. By the 20th century, Einstein began reconceptualizing gravity with his theory of General Relativity, where gravity alters the curvature of local spacetime. From this, we get the principle of locality, which states that an object is directly influenced by its surroundings, and distant objects cannot communicate instantaneously.
However, the birth of quantum mechanics has caused yet another conceptualization, as physicists discovered that non-local phenomena not only exist but are fundamental to reality as we know it. This includes quantum entanglement, where the properties of one particle can be transferred to another instantaneously and regardless of distance. In a new study by the International School for Advanced Studies (SISSA) in Trieste, Italy, a team of researchers suggests that Dark Matter might interact with gravity in a non-local way.
The team was led by Francesco Benetti and Giovanni Gandolfi, two Ph.D. students with the Astrophysics and Cosmology Group at SISSA. He was joined by researchers from the Institute for Fundamental Physics of the Universe (IFPU), the National Institute for Nuclear Physics (INFN), and the Institute of Radio Astronomy at the National Institute for Astrophysics (IRA-INAF). Their paper, “Dark Matter in Fractional Gravity. I. Astrophysical Tests on Galactic Scales” (the first in a series dealing with DM interactions), appeared in The Astronomical Journal.
Image of KK 246 (ESO 461-036), a dwarf irregular galaxy residing within the Local Void, taken by Hubble’s Wide Field Camera 3 (WFC3) and Advanced Camera for Surveys (ACS). Credit: NASA/ESA/Hubble/E. Shaya et al.
According to the most widely-held theory of cosmology, Dark Matter is the mysterious mass that makes up about 85% of material in the Universe. This matter does not interact with baryonic matter (aka. normal or “visible” matter) through electromagnetism or nuclear forces, only gravity (the weakest fundamental force). It was present shortly after the Big Bang, where it formed halos that caused all the neutral hydrogen to gather into clumps, giving birth to the first stars in the Universe that were bound together to create the first galaxies.
In theory, DM is a fundamental component of nature, responsible for the formation of cosmic structures ranging from galaxies to galaxy clusters. It is also responsible for the rotational curves of galaxies, which causes the stars in a galaxy’s disk to orbit around a common center. Its existence is also required for General Relativity, which has been endlessly verified through observation and experimentation, to work on the largest scales. However, the nature of DM remains a mystery in terms of its composition (WIMPs or Axions?) and how it interacts with smaller galaxies.
According to the authors, their study proposes a new model of non-local interaction between the DM of a galaxy and gravity, which could provide a fresh perspective on the still-mysterious nature of this invisible mass. As Einstein said, when describing General Relativity in a nutshell, “Matter tells spacetime how to curve, and curved spacetime tells matter how to move.” As Benetti described his team’s theory to Universe Today via email, “In the innermost part of small galaxies, Dark Matter behaves like a non-local object, interacting with all the other masses in the Universe.”
This stands in contrast to the predominantly held view that Dark Matter is “cold,” meaning that it is composed of weakly interacting massive particles (WIMPS). These particles move slowly relative to the speed of light and interact with normal matter weakly and locally. As Benetti indicated:
“Although the most used model of Dark Matter (the so-called Cold Dark Matter, CDM) gives predictions that are well confirmed by experimental data at a cosmological scale, it suffers issues within galaxies, especially in the cores of the smallest ones. Our model is able to overcome these issues by proposing a non-local interaction between Dark Matter within galaxies.”
The Hubble eXtreme Deep Field (XDF) combines Hubble observations taken over the past decade of a small patch of sky in the constellation of Fornax. Credit: NASA/ESA/UCSC/Leiden University/HUDF09 Team
To model their non-locality theory of DM, the team employed fractional calculus, a branch of mathematical analysis first developed in the 17th century. In recent years, fractional calculus has been found to have applications in various areas of physics but has never been tested in astrophysics before. When used to describe DM in a confined system (small-sized galaxies), this non-locality emerges as a collective behavior of particles. Benetti and his colleagues applied their theory to the rotational curves of thousands of different types of galaxies – from small DM-dominated dwarfs to large spirals.
Their results showed that their theory could predict the rotational velocity of galaxies (Especially smaller ones) better than CDM in Newtonian gravity – which they confirmed by employing a Bayesian statistical analysis. Said Benetti:
“In particular, the theory correctly predicts many scaling laws observed in galactic environments (the radial acceleration relation, core surface density vs. core radius, core radius vs. disk scale length) and that the Dark Matter density should be suppressed n the center of Dwarf galaxies with respect to that predicted by a Cold Dark Matter model in Newtonian gravity. This is confirmed by observations and represents one of the biggest issues in Cold Dark Matter models in Newtonian gravity.”
In particular, the theory proposed by Benetti and his colleagues could provide clues to what is known as the “Cusp-Core Problem” (or “Cuspy Halo Problem”). This refers to the discrepancy between the inferred DM density profiles of low-mass galaxies and the density profiles predicted by cosmological simulations. Several possible solutions have been proposed for this problem, including possible feedback mechanisms to alternate theories of DM (including the possibility it could be “warm”).
The non-locality theory proposed by Benetti and his team offers a potentially revolutionary solution within the CDM framework and could have significant implications for cosmology. “Moreover, if the mechanism by which Dark Matter develops non-local behaviors in these systems is the result of quantum nature, it would represent an example of a quantum system on macroscopic, galactic scales, a very interesting phenomenon on its own,” Benetti added. “Notably, other models of Dark Matter of quantum nature are already known to the community, but none of them introduce a non-local interaction via a fractional derivative.”
This research is part of a growing effort to constrain the nature of Dark Matter and Dark Energy, two of the greatest mysteries facing astronomers and cosmologists today. These efforts will benefit significantly from next-generation telescopes like the ESA’s Euclid mission (which launched earlier today!) and the Nancy Grace Roman Space Telescope (RST), which is scheduled to launch by 2027.
Further Reading: SISSA
