Some neutrinos are fermions. There are quite of few of them out there. Could their degeneracy pressure give rise to an expansion force to explain Dark Energy?

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    $\begingroup$ Good question, only maybe sub-optimally formulated. I tried to fix it. Welcome! $\endgroup$
    – peterh
    Feb 12 '19 at 15:36
  • $\begingroup$ Yes, good question Gary. I've heard this mooted about photons in a paper. I'll try to dig it out. $\endgroup$ Feb 13 '19 at 12:23

There are several reasons dark energy cannot be pressure due to the Pauli exclusion principle. First of all, pressure does not cause expansion of the universe, because pressure is not a force-- pressure gradients are a force (per unit volume), and the cosmological principle precludes them. Indeed, the pressure that exists everywhere only appears as a force when it is put into gravity, and there it is an attraction if it is positive, as it is for what you mean by Pauli pressure. So what you'd need for dark energy is negative pressure, appearing in the gravity.

The second reason is that not only is what you mean by Pauli pressure positive, not negative, it is not any different from normal gas pressure, in the sense that it appears as a consequence of kinetic energy density in exactly the same way as any gas pressure does. This is widely misunderstood, many people think there is some kind of extra pressure that comes from the Pauli exclusion principle, but this is not the case if you simply track the kinetic energy involved. If you are tracking the kinetic energy, then gas pressure is 2/3 the kinetic energy density for nonrelativistic particles, and 1/3 for relativistic, and that's all-- it's just the same for "Pauli pressure," there's nothing at all different about it when you track kinetic energy density-- which is generally exactly what you want to do when you have an adiabatic expansion such as for the universe. Hence, in order for us to understand the pressure from neutrinos, we only need to understand their kinetic energy density, which we think we do because it's pretty easy to track given some assumptions about how neutrinos couple to matter and what their mass is.

You might be wondering, if there's nothing different or extra about "Pauli pressure," then when can it be treated as an extra source of pressure? Only when you are talking about the temperature, rather than the energy. If for some reason it made sense to think of temperature as the fundamental constraint, rather than energy, then it would make sense to think of the Pauli exclusion principle as adding pressure. But even then it's kind of a strange way to think about it, because all the Pauli principle does is constrain how the energy gets partitioned, which in turn affects the temperature. The chain of causality in any gas is energy + partition -> temperature and energy -> pressure independently of temperature, so it's kind of weird to do what is often done, and pretend that temperature + partition -> pressure. It's only that last way that makes degeneracy look like an added pressure, and it would only make sense in a system whose temperature is, for some reason, being controlled. That is rarely the case in an expanding universe, where the temperature is just whatever it needs to be given the energy and the contraints on its partitioning.

  • $\begingroup$ Also, dark energy is apparently constant density, so there would need to be a mechanism to bring new particles out from nothing for any new space “created” by expansion $\endgroup$
    – tuomas
    Feb 12 '19 at 20:05

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