More than three centuries after Isaac Newton laid out his law of gravitation, cosmologists have verified it utilizing the largest objects in the cosmos. Newton’s renowned inverse-square law has long been confirmed through both laboratory testing and within the confines of our Solar System. A new study, detailed in Physical Review Letters, extends this law to the grandest conceivable scales: galaxy clusters separated by hundreds of millions of light-years.
“We know this theory works remarkably well on Earth and within individual galaxies,” states astrophysicist Priyamvada Natarajan. “They are testing it on cosmological scales now.” While the result isn’t surprising, it intensifies the pressure on the alternative Modified Newtonian Dynamics (MOND) theory, which alters gravitational effects to account for the existence of dark matter—the invisible substance whose gravity seems to bind stars within galaxies.
Newton’s law posits that the gravitational attraction between two massive bodies diminishes in inverse proportion to the square of the distance separating them. Published in his 1687 Philosophiæ Naturalis Principia Mathematica, this equation immediately enabled Newton to account for planetary orbits, as quantitatively described by Johann Kepler’s three empirical laws of planetary motion. A century later, Henry Cavendish confirmed the law in a lab setting by suspending a small dumbbell on a fine thread and bringing other weights near its ends. By measuring the wire’s torsion, he determined how the minuscule gravitational force between the weights varied with their separation. Today, physicists perform refined versions of Cavendish’s experiment seeking deviations from the inverse-square law that might signal novel, short-range forces.
Now, researchers, utilizing the Atacama Cosmology Telescope (ACT) in Chile, have turned similar experiments in the opposite direction, toward the largest imaginable scales. “Galaxy clusters are literally the largest structures in the Universe,” notes the study’s lead author, cosmologist Patricio Gallardo of the University of Pennsylvania. Each of these clusters can contain hundreds of galaxies bound by mutual gravity. A cluster might weigh a quadrillion times the mass of the Sun and span tens of millions of light-years.
The researchers examined the interactions of hundreds of thousands of clusters by statistically combining measurements of their positions and velocities. Analogous to how planets closer to the Sun orbit faster, two clusters nearer to each other will move faster relative to one another, explains study co-author and cosmologist Chris Parido of the University of Southern California. Therefore, by observing how the relative velocity between any two clusters changes with their separation, the nature of gravity can be probed.
But not in a straightforward manner. The relative speed of two clusters is influenced not only by the gravitational pull they generate themselves but also by the gravity of all surrounding clusters. To account for this complexity, the researchers first sourced data on the spatial distribution of galaxies from the Sloan Digital Sky Survey (SDSS), which has mapped millions of galaxies since 2000. They applied a generalized force law, fitted with adjustable parameters, to this spatial distribution to forecast how the relative velocity of cluster pairs would change with distance.
Next, the scientists compared this prediction against velocity data gathered by the ACT instrument, which operated from 2007 to 2022. The ACT measured the afterglow of the Big Bang, the Cosmic Microwave Background (CMB), and proved particularly effective at detecting galaxy clusters. When CMB photons pass through a galaxy cluster, they scatter off electrons within it, gaining or losing energy depending on whether the cluster is moving toward or away from Earth—a phenomenon known as the kinematic Sunyaev-Zel’dovich (kSZ) effect. This effect makes clusters easily detectable and offers a direct probe of their velocities.
To circumvent confounding effects related to the Universe’s expansion and the space-stretching dark energy, the researchers concentrated on galaxy clusters positioned between 5.6 and 7.7 billion light-years away—a snapshot of cosmic time. According to Parido, the team investigated accelerations as small as 10 femtometers per second squared, which is one quadrillionth of Earth’s gravity. Over distances spanning 80 to 800 million light-years, the gravitational force varied like one over the distance to the power of 2.1, plus or minus 0.3, offering clear confirmation of Newton’s law of gravitation.
Newton’s victory comes at the expense of the MOND theory. Proposed in the 1980s to bypass the necessity of dark matter, MOND does not modify Newton’s law of gravity but instead changes Newton’s second law of motion—force equals mass times acceleration—under conditions of extremely low acceleration. However, if MOND were correct, on the largest scales, gravity would effectively vary as one over the distance, rather than one over the square of the distance. MOND already struggles to describe universal evolution, and this new data delivers another blow, Gallardo comments.
Perhaps more significantly, the study validates the capability of measuring velocities using the kSZ effect, Parido suggests. The successor to ACT, a microwave telescope array called the Simons Observatory, has begun collecting data. It will measure the kSZ effect with far greater precision, providing a tool to track dark energy and the history of the Universe’s expansion, Parido adds. “Much more can be done with this method.”
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