Researchers from Vanderbilt University in Nashville have come up with a new mathematical formulation that they say will help reconcile the classic notion of viscosity based on the laws of thermodynamics with Einstein’s general theory of relativity.
Their work, published earlier this year in the journal Physical Review D, should help determine just how “sticky” the universe is by explaining cosmological viscosity in a “simpler” and “more elegant” way while still being “mathematically sound” and obeying “all the applicable physical laws,” study co-author and physics professor Robert Scherrer said in a statement.
The new formula was developed by Marcelo Disconzi, an assistant professor of mathematics at Vanderbilt, along with Scherrer and fellow physics professor Thomas Kephart. It addresses the issues with cosmological viscosity by starting with the issue of relativistic fluids, a phenomenon produced by supernovae and the crushed, planet-sized stars known as neutron stars.
While scientists have previously successfully modeled what happens with ideal fluids, or those with no viscosity, most fluids are viscous in nature, and to date, nobody has managed to devise an accepted way to handle viscous fluids traveling at relativistic velocities. Past models used to predict what happens when these realistic fluids are accelerated to a fraction of the speed of light have been plagued by multiple blatant inconsistencies.
Building upon previous studies of cosmological viscosity
The problems with these models inspired Disconzi to tweak the equations of relativistic fluid dynamics in such a way that it does demonstrate those inconsistencies, including one glaring flaw in which they predicted conditions where these fluids were capable of traveling faster than the speed of light, which the professor called “disastrously wrong.”
“Strictly speaking, I did not come up with the formulation myself,” he told redOrbit via email. Rather, he said that he demonstrated that a previous proposal advanced by mathematician André Lichnerowicz in the 1950s “is a viable candidate for a theory of relativistic viscous fluids,” then teamed up with Scherrer and Kephart to “investigate formalism in the context of cosmology.”
“It is not known how to describe viscous fluids in the context of general relativity (GR),” he continued. “Over the years different approaches have been proposed,” including the Mueller-Israel-Stewart theory. While that proposal “does lead to a satisfactory description” in several situations, Disconzi explained that it also “contains some ad hoc features and ultimately does not completely rule out the existence of faster-than-light signals.”
Disconzi said that Lichnerowicz’s proposal remained largely unnoticed until he published a paper on the topic last year. That study “by no means settles the question of what the correct formulation of relativistic viscous fluids is,” he told redOrbit. “What it shows is that, under some assumptions, the equations put forward by Lichnerowicz have solutions and the solutions do not predict faster-than-light signals. But we still don’t know if these results remain valid under the most general situations relevant to physics.”
Implications for dark energy, ultimate fate of the universe
The formula described in the new study could also have significant implications for the ultimate fate of the universe, the university explained in a statement. Furthermore, it could shed new light on the basic characteristics of the unusual form of repulsive energy known as “dark energy,” the substance used to explain the accelerating expansion of the cosmos.
Since it was first discovered in the 1990s, there have been several theories that have attempted to explain the nature of dark energy, but most of them have failed to account for cosmic viscosity, the study authors explained. Disconzi said that it’s possible, but unlikely, that viscosity might be able to account for all of the acceleration that has been attributed to dark energy. It is more likely responsible for at least “a significant fraction of the acceleration,” he added.
Furthermore, the study also seems to support a radical scenario designed to address the ultimate fate of the universe, known as the “Big Rip.” This scenario proposes that the universe contains a phantom-type of dark energy that grows stronger over time, causing the expansion rate of the universe to become so great that material objects ultimately fall apart, causing individual atoms to disassembled and themselves into unbound elementary particles and radiation.
In this scenario, the universe will fall apart if the ratio between the pressure and density of dark energy (its equation of state parameter) falls below -1 – a value known by cosmologists as the “phantom barrier.” In previous models with viscosity, the “Big Rip” was impossible, because the universe could not evolve beyond the limit. In the new formulation, however, the barrier does not exist and viscosity actively drives the universe towards this specific end state.
So does that make the “Big Rip” scenario the most likely scenario when discussing the ultimate fate of the universe? “The fair answer is that nobody really knows,” Disconzi explained to redOrbit. “What is known from current observational data is that a ‘Big Rip’ scenario is possible, although the available data is far from conclusive. What our paper brings to the discussion is a mechanism that yields a ‘Big Rip’ in a fairly natural way, in contrast of most models of the ‘Big Rip’ where unnatural or ad hoc assumptions have to be introduced.”