Neutrinos from the big bang can probe magnetic fields and gravitational inhomogeneities in the early universe

7/1/2021 3:22:48 PM Gordon Baym and Jen-Chieh Peng

The magnetic field in the Whirlpool Galaxy (M51), measured by the NASA SOFIA infrared observatory, superimposed on a Hubble telescope picture of the galaxy. This image illustrates characteristic magnetic fields of galaxies that can modify neutrino helicities. (Credit: NASA)
The magnetic field in the Whirlpool Galaxy (M51), measured by the NASA SOFIA infrared observatory, superimposed on a Hubble telescope picture of the galaxy. This image illustrates characteristic magnetic fields of galaxies that can modify neutrino helicities. (Credit: NASA)

 

Neutrinos decoupled from matter in the early universe at around one second after the big bang. These relic, or primordial, neutrinos have been propagating through the universe ever since. Quite amazingly, their present density is about 337 per cubic centimeter; 10 million or so of these big bang remnants are in our bodies at any one time. By comparison there are only one-hundredth as many solar neutrinos per cubic centimeter on Earth. As we discuss in two newly-published papers, relic neutrinos can be unique messengers of conditions in the early universe, including primordial density inhomogeneities and cosmic as well as later galactic magnetic fields.

  

We have learned in recent years through study of neutrino oscillations at reactors and underground experiments, that the masses of at least two of the neutrino mass states are non-zero. We understand details of how the three neutrino states—electron-like, muon-like, and tau-like—that take part in weak interactions are in fact linear superpositions of three fundamental mass states. However, certain basic questions about neutrinos have yet to be answered: Which of the mass states is most strongly present in the electron neutrino (the "neutrino mass hierarchy" problem)? And very fundamentally, are neutrinos Dirac fermions with distinct antiparticles, or Majorana fermions, which are their own antiparticles? 

 

Because the temperature of primordial neutrinos at present is about 1.9K—smaller than the Cosmic Microwave Background (CMB) temperature of 2.7K—relic neutrinos in two of the three mass states are, surprisingly, non-relativistic now, with velocities lower than 1/50 the speed of light.  

 

The temperatures at which neutrinos decouple in the early universe are of order 1010 larger than the neutrino masses. Thus, according to the standard model, neutrinos are predominantly in negative helicity states, i.e., with the spins pointing opposite to their momentum, while antineutrinos are predominantly in positive helicity states, with their spin and momentum parallel. As neutrinos propagate past density inhomogeneities, their trajectories are bent—the gravitational lensing of neutrinos. As the momenta are bent, their spins, according to general relativity, bend less. Consequently, even if a neutrino starts with negative helicity it develops an amplitude to have positive helicity.

[cr][lf]Fig. 1: The root mean square bending angle of the spin of a primordial neutrino with respect to its momentum from gravitational vs. magnetic effects, as a function of the neutrino mass, with ÃŽ¼ÃŽ½Â the neutrino magnetic moment  and ÃŽ¼B the Bohr magneton.   [cr][lf]
Fig. 1: The root mean square bending angle of the spin of a primordial neutrino with respect to its momentum from gravitational vs. magnetic effects, as a function of the neutrino mass, with µν the neutrino magnetic moment and µB the Bohr magneton.

 

In addition, neutrinos are expected to have a magnetic moment. Thus, as they propagate through the magnetic fields in the cosmos, their spins precess about the magnetic fields, while their momenta do not change. (More technically only Dirac neutrinos have the kind of (diagonal) magnetic moment that would be sensitive to the slowly varying cosmic magnetic fields.) This process also gives neutrinos an amplitude to have positive helicity. The magnetic and gravitational processes, as we calculate, implant on primordial neutrinos a record of the gravitational and magnetic fields they have propagated through en route to Earth (see Fig. 1). The gravitational effect depends on the autocorrelation function of density fluctuations, while the magnetic effect depends on the autocorrelation functions of cosmic and galactic magnetic fields.  

 

The magnetic effect also depends on the neutrino magnetic moment. A moment as small as that predicted in the standard model would have negligible effect. However, the magnetic moment could be orders of magnitude larger, owing to non-standard model physics. Indeed, one possible explanation for the excess of low energy electron events, below some 7 keV, seen in the XENON1T experiment, is a magnetic moment more than a billion times larger than the standard model estimate. Neutrinos with such a large moment have their spins and helicities completely randomized by cosmic magnetic fields.

 

Fig. 2:  The detection rate of primordial neutrinos is proportional to the coefficient A<sub>eff</sub>, plotted here versus the mass of the lightest neutrino, for Dirac and Majorana neutrinos and for the normal (NH) and inverted (IH) hierarchies. The dashed curves show the extreme case of complete helicity flip from left to right handed. The dash-dot curve shows the result for Dirac NH neutrinos under some assumptions of the magnetic field of the Milky Way and the neutrino magnetic moment.
Fig. 2:  The detection rate of primordial neutrinos is proportional to the coefficient Aeff, plotted here versus the mass of the lightest neutrino, for Dirac and Majorana neutrinos and for the normal (NH) and inverted (IH) hierarchies. The dashed curves show the extreme case of complete helicity flip from left to right handed. The dash-dot curve shows the result for Dirac NH neutrinos under some assumptions of the magnetic field of the Milky Way and the neutrino magnetic moment.

Relic neutrinos have yet to be detected. The most promising way to detect them is by means of the inverse tritium beta decay process, in which a tritium (3H) nucleus absorbs an electron-like neutrino, emitting an electron and turning into a 3He nucleus. The rate is sensitive to whether neutrinos are Dirac or Majorana, to the neutrino mass hierarchy, and to the helicity of the neutrinos (see Fig. 2). If neutrinos are Majorana, the capture on tritium does not depend on either the mass hierarchy or the neutrino helicity. However, if neutrinos are Dirac and the hierarchy is normal—that is, the lowest mass state is strongly present in an electron neutrino—the inverse tritium process can reveal how helicities of relic neutrinos are modified by the magnetic fields and matter distributions in their journey from the big bang to now.

 

 

 

For more information, you can find the original papers here:

G. Baym and J. C. Peng,  Evolution of Primordial Neutrino Helicities in Astrophysical Magnetic Fields and Implications for their Detection, Phys. Rev. Lett. 126, 191803 (2021).

G. Baym and J. C. Peng, Evolution of Primordial Neutrino Helicities in Cosmic Gravitational Inhomogeneities, Phys. Rev. D 103, 123019 (2021).