Big Bang: Limits on Neutrino Masses

At first sight, it may seem very difficult to say anything meaningful about what happened in the first second after the creation of the universe in the big bang. However, such an understandable reaction is not correct. In astrophysics, there are many cases where it is easier to understand something that is quite remote from us in space and time than something that is right at hand. A case in point is the fact that we know much more about the constitution of the core of the Sun than that of the core of the Earth. Even though the latter is much closer to us, the physics of partly molten and partly solid mixtures of iron and nickel and other chemical elements is highly complex. In contrast, the much higher temperature in the center of the sun guarantees that all matter there is broken down into much simpler constituents that are far easier to describe. Similarly, the conditions in the very first few seconds and minutes after the big bang are yet simpler than the conditions in the center of the sun. Therefore, we are quite confident that we can not only meaningfully describe what happened just after the big bang, but that we can even use those descriptions to put limits on the number and type of elementary particles that are exist.

An Excluded Range, from 50 eV to 10 GeV

The basic idea is that all particles that are not too heavy, and that couple strongly enough, were present in the heat bath that filled the universe in very early times. Particles that are much more massive than the equivalent thermal energy per degree of freedom may have annihilated with their antiparticle partners, while particles that do not interact often enough may have decoupled from the heat bath. But all other particles would have been present, and if there had been too many of them, or if some of them had been too heavy, their total mass would have exceeded the bounds that astrophysical observations have put on them.

Using such arguments, I realized that stable neutrinos could not exist with masses between 50 eV and 10 GeV. In published my result in the paper

Similar conclusions were reached around the same time by Ben Lee and Steven Weinberg and others. This was the first paper I wrote in the area of what later became known as astroparticle physics but was just emerging then. One of my two thesis advisors at that time, Tini Veltman, formed a rich source of inspiration for me, something I reflected upon much later after he and Gerard 't Hooft received the Nobel prize in 1999, in a paper Vuurwerk van Tini (Tini's Fireworks; in Dutch), by Hut, P., 1999, Nederlands Tijdschrift voor Natuurkunde, 65, pp. 356-358.

In the three decades since I wrote my 1977 paper, the limits on light neutrinos have become significantly more stringent. Recent results are quoted in a paper by Thomas et al. who give a strong 95% confidence upper limit to the sum of neutrino masses of 0.28 eV.

Another Excluded Range, beyond 60 GeV

My first bound on neutrino masses was pretty much independent of any details of the underlying field theories. However, if one assumes that grand unified theories are responsible for the creation of baryons in the universe, an extra bound can be found. Keith Olive and I realized this while we attended a summer school as graduate students, and we published our findings in the proceedings of the school as:

We also summarized our results in the paper:

  • A Cosmological Upper Limit on The Mass of Heavy Neutrinos, by Hut, P. & Olive, K.A., 1979, Phys. Lett. 87B, 144-146.

Decaying Neutrinos

The previous bounds all applied to stable neutrinos. If some neutrino species would be unstable, combined bounds can be found for their mass and life time, as we showed in a paper:

The possible presence of decaying neutrinos complicates the usual cosmological arguments concerning the relations between the matter content and the expansion of the universe. I had already published a generalization of those arguments in: Cosmological Tests of General Relativity, by Hut, P., 1977, Nature 267, 128-130.