“This initiative is in turn driven by my frustration with the status quo, namely the notion of dark matter’s existence despite the lack of any direct evidence for a whole century,” said Richard Lieu, a professor of physics and astronomy at the University of Alabama at Huntsville, in a recent press release issued by the Monthly Notices of the Royal Astronomical Society. Lieu’s radical suggestion gravity without mass is fueling a fresh wave of debate among physicists and cosmologists who long have struggled with the universe’s missing mass.
Astronomers have for decades observed stars on the periphery of galaxies move at velocities that are impossible under the gravity caused by visible matter only. The standard answer has been dark matter: an unseen, unknown substance estimated to make up some 85% of the universe’s matter content. But even after huge experimental efforts were expended, no direct detection of dark matter particles has been made.
Lieu’s explanation takes a turn away from invisible particles and toward the mathematical structure of spacetime itself. He proposes that shell-like topological defects structures with an inner skin of thin positive mass and an outer skin of thin negative mass can produce gravitational forces without possessing overall mass (such shells have a force on stars within them). In Lieu’s own words, “the total mass of both layers — whichis all one could measure, mass-wise is exactly zero, but when a star lies on this shell it experiences a large gravitational force pulling it towards the center of the shell.”
The mathematical basis for this concept arises from a second, previously unappreciated solution to the gravitational Poisson equation. Whereas Newton’s law of gravity defines a force that decreases as the square of distance (1/r²), Lieu’s model shows us that a massless shell can generate an attractive force which falls off only as 1/r. When numerous such shells are placed concentrically, the resulting gravitational field can power the flat rotation curves seen in galaxies, which long ago were thought to be due to dark matter.
This theory also provides a new explanation for gravitational lensing the deflection of light by heavy objects. In the past, lensing seen in areas devoid of visible mass has been attributed to dark matter. Lieu’s shells, however, can sequentially deflect light as it passes through each layer, producing a cumulative effect that mimics the lensing signature of a massive, invisible halo (the model predicts a constant inward deflection angle, matching that of an isothermal sphere). The unique prediction in this case is that lensing occasionally needs to exhibit exceptionally large fluctuations when a light path skims a shell a test that can be used to distinguish this model from run-of-mill dark matter models.
However, the physical cause of these topological defects is still uncertain. It has long been theorized that the early universe experienced a sequence of symmetry-breaking phase transitions, as water solidifies into ice, under which stable defects like cosmic strings, domain walls, and monopoles may have emerged (phase transitions in the early universe; the generation of topological defects). Lieu’s model involves a particular type of shell defect whose creation mechanism is not yet known. Partial support also arises from the discovery of giant arcs and ring-like configurations in the overall distribution of galaxies at large scales, which could be indicative of such defects.
The proposal joins a busy set of dark matter alternatives. Modified Newtonian Dynamics (MOND) and its relativistic cousins such as TeVeS have sought to modify gravity itself, frequently succeeding in describing galactic rotation curves but failing at gravitational lensing and the cosmic microwave background (MOND’s range and limits). Lieu’s model, on the other hand, keeps the general relativistic framework but fills spacetime with exotic defects that can, in principle, be probed by astrophysical observations.
Massless shell defects mathematics is firm in the weak-field regime and stable for Einstein’s field equations. The model even includes the interaction with common baryonic matter, and observed rotation curves can be matched when baryons remain in hydrostatic equilibrium with the shell-created potential.
Even with its beauty, Lieu’s theory has a serious drawback. Foremost among them is the fact that there is no clear mechanism for the creation of such defects during cosmological phase transitions, and no direct observational evidence for their presence. As Lieu himself warns, “it is unclear presently what precise form of phase transition in the universe could give rise to topological defects of this sort.”
The quest for the missing mass of the universe goes on, but with every new theory, the world is cautioned that the universe might yet have surprises in store in the very nature of spacetime itself.
