Testing theories of modified gravity

The accelerated expansion of the universe is usually attributed to a mysterious dark energy, but there’s another conceivable explanation: modified gravity. Unmodified gravity—that is, Einstein’s general relativity— satisfactorily accounts for the dynamics of the solar system, where precision measurements can be made without the confounding influence of dark matter. Nor have any violations been detected in one of general relativity’s principal ingredients, the strong equivalence principle, which posits that inertial mass and gravitational mass are identical.

But those observational constraints are not ineluctable. In particular, a class of gravitational theories called Galileon models can also pass them. In 2012 Lam Hui and Alberto Nicolis of Columbia University devised a cosmic test that could refute or confirm the models. Their test hinges on the models’ central feature: an additional scalar field that couples to mass. The coupling can be characterized by a charge-like parameter, Q. For most cosmic objects, Q has the same value as the inertial mass. But for a black hole, whose mass arises entirely from its gravitational binding energy, Q is zero; the strong equivalence principle is violated.

Galaxies fall through space away from low concentrations of mass and toward high concentrations. The supermassive black holes at the centers of some galaxies are carried along with the flow. But if gravity has a Galileon component, the black hole feels less of a tug than do the galaxy’s stars, interstellar medium, and dark-matter particles. The upshot, Hui and Nicolis realized, is that the black hole will lag the rest of the galaxy and slip away from its center. The displacement is arrested when the black hole reaches the point where the lag is offset by the presence of more of the galaxy’s gravitational mass on one side of the black hole than on the other. Given the right circumstances, the displacement can be measured.

Hui and Nicolis’s proposal has now itself been put to the test. Asha Asvathaman and Jeremy Heyl of the University of British Columbia, together with Hui, have applied it to two galaxies: M32, which is being pulled toward its larger neighbor, the Andromeda galaxy, and M87 (shown here), which is being pulled through the Virgo cluster of galaxies. Both M32 and M87 are elliptical galaxies. Because of their simple shapes, their centroids can be determined from optical observations. The locations of their respective black holes can be determined from radio observations. Although the limit on Galileon gravity that Asvathaman, Heyl, and Hui derived was too loose to refute or confirm the theory, they nevertheless validated the test itself. More precise astrometric observations could make it decisive. (A. Asvathaman, J. S. Heyl, L. Hui, Mon. Not. R. Astron. Soc. 465, 3261, 2017, doi:10.1093/mnras/stw2905 .)