## The cosmic expansion towards the Big Rip

Three physicists from Vanderbilt University have introduced a new mathematical formulation to treat fluid dynamics relativistic. The study, published in Physical Review D, has important implications for the ultimate fate of the universe and could shed light both on the nature of dark energy. Although this is a promising approach, however, it needs further analysis in order to verify whether or not the accuracy of the results.

The Universe could be a place somewhat “tacky”, but how tacky is a debated issue. This is because for decades cosmologists have faced a number of difficulties in order to reconcile the classical notion of viscosity based on the laws of thermodynamics to the theory of general relativity. Today, however, three physicists from Vanderbilt University have introduced a new mathematical formulation of the problem that seems to reduce this gap. The findings, published in Physical Review D, have important implications for the ultimate fate of the Universe as they tend to favor one of the cosmological scenarios more radical: we are talking about the “Big Rip”. Not only that, but this study could shed light on the mystery of dark energy.

The idea to approach this problem has been developed by the mathematician Marcelo Disconzi in collaboration with two colleague physicists Thomas Kephart and Robert Scherrer. “Marcelo has introduced a mathematical formulation more simple and elegant, consistent with all laws of physics,” says Scherrer. The type of viscosity we are talking about, and that has cosmological significance, is different from the one we are most familiar and it is called “shear viscosity” (think ketchup), a measure of the resistance of a fluid to pass through small openings, like the neck of a bottle. In our case, however, it is a form of viscosity dilatational, which represents the degree of resistance of a fluid to an expansion or contraction. The fact that often we do not have to do with this type of viscosity in the life of all days is due to the fact that most of the liquids cannot be too compressed or expanded.

**Credit:** Jeremy Teaford / Vanderbilt

Disconzi has begun to address the problem of relativistic fluids. The astrophysical objects that produce this phenomenon are typically stellar explosions (supernovae) and neutron stars (super dense, compact objects that can have the typical size of a planet). Scientists have achieved remarkable successes in describing the dynamics of an ideal fluid, where there is no viscosity, when it is accelerated to speeds approaching that of light. But in nature, almost all fluids are viscous and, despite years of theoretical efforts, no one has addressed the problem of treating the dynamics of viscous fluids when it has to do with relativistic speeds. In the past, the models formulated to predict what happens when more realistic fluids are accelerated until they reach some fraction of the speed of light have given a number of inconsistencies: for example, the most obvious concerns the prediction that under certain conditions these fluids could propagate even with faster than the speed of light. “This is absolutely wrong,” says Disconzi, “since it is well established experimentally that nothing can travel faster than light.” So, these issues have inspired the scientist to reformulate the equations of fluid dynamics relativistic so that you do not have flaws that lead to results contrary to the theory of special relativity. To do this, Disconzi started from the hypothesis advanced in the 50s by the French mathematician André Lichnerowicz and then called for the collaboration of colleagues Kephart Scherrer and to apply his equations with a cosmological theory more generally. This has resulted in a number of interesting results, including some new, potential clues about the mysterious dark energy.

In the 90s, the physics community was shocked when the astronomical measurements of Type Ia supernovae showed that the Universe is expanding at an accelerating pace. To explain this unexpected phenomenon, scientists were forced to assume the existence of an unknown form of energy that permeates all space repulsive. Given our ignorance of its nature, it was given the term “dark energy”, by analogy with the “dark matter” another great mystery of modern physics. So far, the main theories of dark energy did not take into account the problem of “stickiness cosmic”, despite the fact that it has a repulsive effect strikingly similar to the one created by dark energy. “It’s possible, though not very likely, that the presence of viscosity can take into account all the effects of the acceleration attributed to dark energy,” says Disconzi. “It’s much more likely that a significant fraction of the effect of the acceleration space, may be due to a direct cause. In other words, the same viscosity could be a major constraint to the properties of dark energy.”

Another interesting finding relates to the ultimate fate of the Universe. Since the discovery of the accelerated expansion, cosmologists have suggested a number of scenarios for groped to describe the future evolution of the cosmic expansion. One of them, called “Big Freeze” (The big freeze), predicts that after about 100 thousand billion years the universe will become so great that the gas supplies needed to form the stars will be exhausted long ago. The stars will go out gradually, leaving only holes blacks who, in turn, will evaporate slowly as space becomes more and more cold. But a scenario even more dramatic is called the “Big Rip” (the big wrench). It is based on the effects due to dark energy that becomes increasingly important over time. In this case, the rate of expansion of the universe will become so high that after little more than 20 billion years all matter will begin to disintegrate and, in turn, also the atoms will separate in their fundamental constituents leaving behind only elementary particles and radiation.

The fundamental key that comes into play in the latter scenario is the relationship between the pressure and the density of dark energy that is the parameter of its equation of state. If this value becomes less than -1, then the universe will eventually disintegrate completely. Scientists have defined this parameter as a sort of “barrier ghost”, i.e. a limit that in previous models with a viscosity cannot be exceeded. However, in the formulation of Desconzi-Kephart-Scherrer this limit does not exist. Instead, this barrier provides the parameter of the equation was a natural way to take on values less than -1. “In previous cosmological models with viscosity, the Big Rip was not possible,” adds Scherrer. “But in our model, it is the viscosity that drives the evolution of the Universe to a state final extreme.”

In short, according to the authors, the results of this new mathematical formulation in the case of relativistic viscosity are very promising but need further study to see whether or not their veracity. The only way to do this will be to use powerful computers to analyze numerically complex equations. In this way, scientists will be able to make predictions that can be compared with experiments and any comments.