A number at last!

I finally have a number. The Friedmann equations together with measurements as a first “guess” seem to permit the expanding universe to have a viscosity as large as about ~ 10^6 Pa s (positive or negative).  1 000 000 Pa s, if you like zeros (and btw; Pa s=kg/(m s)). The shear viscosity of the much denser fluid called “water” (perhaps you encountered it?) is of the order +10^-3, and the bulk viscosity is typically much smaller. The extremely slowly floating fluid called pitch, has a viscosity “only” a hundred times greater (~10^8 Pa s) than that which I here suggest for the universe; the so-called cosmic fluid. This, therefore, is so far a rather peculiar result. So peculiar that it took some time discussing with my supervisor before he quit believed it. You know; I didn’t really have any grasp on how big those numbers ought be, so I just ran over with my results in shear (or perhaps bulk) joy of finally having a number. OK… IT DID strike me as a rather large number, but the universe is extremely large so.. (hehe)…and… I had a number! After months of trying and failing with adding and subtracting letters from the Norwegian and Greek alphabet, the taste of a number is sweet and welcomed — even for a theorist. After all you gotta bow for experiments, and if your theories doesn’t predict anything, there is no way you can test against observations, is there.

This
Figure 1: Evolution of the Hubble parameter with red-shift when the viscosity parameter is B=0.1. Increasing red-shift corresponds to more and more distant past. Red-shift z=-1 equals infinite future. Red-shift z=0 is at present. The blue and red curves visualize the evolution with positive and negative viscosity, respectively, whereas the black curve gives the viscosity-less solution. Note that the bare eye cannot distinguish the three different scenarios.

 

 

 

 

 

 

 

 

 

 

The number might just be wrong, though. After all; does the universe exhibit viscous behavior in the first place? Actually there seems to be strong arguments begging explanations if it does not, rather than having to explain why it should. Refer to arXiv:9602128 for a perhaps non-intuitive , yet (in my opinion) quit reasonable, result to this end: Even two ideal expanding fluids should posses viscosity when described as one fluid.

When all comes down to all, fact seems to be that the upper bound so far obtained not necessarily is so far off as a descriptive viscosity (nothing said about it’s cause). As an upper limit, that is. Adding this viscosity to the Friedmann equations almost doesn’t alter the evolution predicted by the standard model (LambdaCDM) at all. Figure 2 shows the evolution when the model is extended with a viscosity term 10 times larger than an upper bound of 10^6 Pa s. Refer to figure 1 and 2 to see that adding negative viscosity seems to fit the data just as well as adding the corresponding positive amount. Negative viscosity corresponds to energy being pumped into the system, and might sound forbidding on thermodynamic grounds, since it seems to violate energy conservation (in 4 dimensional space-time at least). But it seems my supervisor has been speculating in those directions. Refer to arXiv:1306.5634 for interesting details and cosmological models in which the entropy actually decreases with time. If that is correct, the universe will actually acquire a higher and higher degree of order. That should seem weird to most old-ordered fellows. Well; thanks for being so interested in my thesis’ topic that you actually read it all! I know it is interesting… and I am sure you are just as excited as am I to know how adding viscosity to the universe eventually may (or may not) alter it’s final and non-reversible (?) end. It’s fate. It almost feels like it’s fate is in my hands, but I think I might just be exaggerating a bit there… 😉
I find it intriguing, though, that God (who is the one who really decides the fate of his creation!), has made men so small and insignificant, yet capable of making ups his mind about the fate of the whole thing. The whole mega-giga-parsec creation of billions upon billions of galaxies with billions upon billions of stars. We are the center of the universe, aren’t we?

Evolution of the Hubble parameter with red-shift. Increasing red-shift corresponds to more and more distant past. Red-shift z=-1 equals infinite future. Red-shift z=0 is at present.
Figure 2: Evolution of the Hubble parameter with red-shift when the viscosity parameter is B=1. Increasing red-shift corresponds to more and more distant past. Red-shift z=-1 equals infinite future. Red-shift z=0 is at present. The blue and red curves visualize the evolution with positive and negative viscosity, respectively, whereas the black curve gives the viscosity-less solution.

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