I was trying to make heads of tails of both this paper and the press release about it.

The scientists have used bulk viscosity (as opposed to shear viscosity) and popped it into a model and somehow ended up at the Big Rip.

My question is, how do the two correlate in any way? Have the scientists considered the fabric of space time as a viscous fluid? Have they considered the matter within the universe to be a viscous fluid? I'm stuck on this one clarification: why does it matter that there's a viscous fluid?

  • $\begingroup$ I think they are mostly trying to fix the flaws of a model, but I am not sure that their fix has any more significance than the fact that the model they are trying to fix is broken. The viscous fluid assumption seems to make sense on mesoscopic scales, but will probably clash with general relativity on the largest scale. Naive introduction of friction is probably what breaks Lorentz symmetry... I just can't tell if this is the correct approach to lossy phenomena that can preserve the fundamental properties of GR. $\endgroup$
    – CuriousOne
    Jul 1, 2015 at 16:15
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    $\begingroup$ related: physics.stackexchange.com/q/647825/226902 physics.stackexchange.com/q/730551/226902 physics.stackexchange.com/q/62940/226902 (note: as far as I am aware, in cosmology the relativistic Navier-Stokes dissipative hydrodynamics is not used.. but rather the Israel-Stewart formulation of dissipative fluids). $\endgroup$
    – Quillo
    Oct 11, 2022 at 18:22
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    $\begingroup$ See a recent review on Viscous Cosmology for Early- and Late-Time Universe here: arxiv.org/abs/1706.02543. As @Quillo noted, the Israel-Stewart formulation of dissipative fluids is preferred in Viscous Cosmology. $\endgroup$
    – MadMax
    Oct 11, 2022 at 21:18
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    $\begingroup$ @CuriousOne, dissipative hydrodynamics can be formulated to be consistent with GR, no "clash with GR" (but not the naive extension of Navier-Stokes, see also the comment by @MadMax). See e.g. this answer: physics.stackexchange.com/a/730704/226902 $\endgroup$
    – Quillo
    Oct 11, 2022 at 22:42
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    $\begingroup$ Related: Weinberg, bulk-viscous cosmology-> physics.stackexchange.com/q/779297/226902 $\endgroup$
    – Quillo
    Sep 13, 2023 at 15:10

1 Answer 1


The Universe at a large scale is ruled by Einstein's equations. There is the "gravity part" (possibly with the cosmological constant) and the "matter part" (namely, the energy-momentum tensor).

Now, the energy-momentum tensor should include all the contributions that you may want (the number of ingredients, namely fields, and the complexity of the energy-momentum defines how realistic your model may be).

You should account for baryons, radiation, leptons... all those ingredients are typically treated as "fluids". An important ingredient to be incorporated into the energy-momentum tensor is the "equation of state" of the matter (when a hydrodynamic approach is used to describe matter). Usually, simple choices are made: the energy-momentum tensor is that of a perfect fluid (an even simpler choice is the one of dust).

Of course, you can write down more realistic models by accounting for fluids with more chemical species or dissipative fluids! This should not be surprising: the matter fluid filling the Universe undergoes friction and the Universe's entropy increases.

Bulk viscosity: as the universe expands/contracts the particles/fields in it undergo "chemical" reactions (e.g., the baryogenesis, the Big Bang nucleosynthesis, etc...). This gives rise to bulk viscosity! This is true for both Newtonian as well as for relativistic fluids, see e.g. "Bulk viscosity in relativistic fluids: from thermodynamics to hydrodynamics".


Hiscock, W. A., and Salmonson, J. (1991). Dissipative Boltzmann-Robertson-walker Cosmologies. Phys. Rev. D. 43, 3249–3258.

Maartens, R. (1995). Dissipative Cosmology. Class. Quan. Grav. 12, 1455–1465.

In a seminal paper by Weinberg, he discusses the bulk viscosity, shear viscosity, and heat transport due to radiation in a relativistic fluid. He also evaluates the cosmological entropy production associated with a nonvanishing mean free time of photons and other particles.

An introduction to the relativistic hydrodynamic theory needed to understand these works (relativistic bulk viscosity, heat, radiation hydrodynamics) can be found here: see Section 8.2 for the equations describing a relativistic fluid with bulk viscosity.


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