Primordial Neutrinos' Imprint on the Early Universe

[lpetrich]

Earliest Signal Ever: Scientists Find Relic Neutrinos From 1 Second After The Big Bang noting First constraint on the neutrino-induced phase shift in the spectrum of baryon acoustic oscillations | Nature Physics

When I came across this article I thought that it might be a direct detection. But that would be very difficult for primordial neutrinos, much more difficult than for the ones that we are already able to detect, because of their very low energy. Instead, it is from their gravitational effects on the early Universe. We already know of one such effect, on primordial-nucleosynthesis results, and this recent result is about another, on the Universe's primordial fluctuations. This effect was recently observed in the Cosmic Microwave Background, and it was most recently observed in the Universe's large-scale structure.

So far, these results are consistent with neutrinos having only 3 light flavors: electron, muon, and tau. But since these effects are purely gravitational, primordial gravitational waves and similar sorts of relics can mimic neutrinos, thus yielding an apparent non-integer number of neutrino flavors. So might we someday be able to observe with enough precision to see such effects?

Here is how the present-day Universe divides up:
[TABLE="class: grid"]
[TR]
[TD]Dark Energy[/TD]
[TD]0.683[/TD]
[/TR]
[TR]
[TD]Dark Matter[/TD]
[TD]0.268[/TD]
[/TR]
[TR]
[TD]Baryonic Matter[/TD]
[TD]0.049[/TD]
[/TR]
[TR]
[TD]Photons[/TD]
[TD]0.00006[/TD]
[/TR]
[TR]
[TD]Neutrinos[/TD]
[TD]0.0014[/TD]
[/TR]
[/TABLE]
(Neutrinos' total mass assumed to be 0.06 eV, Hubble constant 67 km/s/Mpc)

Looking back around 13.7 billion years ago, to about 380,000 years after the start of the Universe's expansion, we find recombination, where the Universe has cooled down to about 4000 K, enough for its hydrogen and helium nuclei to capture its electrons. The resulting atoms are much less opaque, and the Universe's photons now flow freely, out of equilibrium. These photons have survived to the present day, though redshifted to a temperature of 2.7 K and observed as the Cosmic Microwave Background.

Something similar happened to neutrinos about 1 second after the Universe expansion's start. When the Universe cooled down to about 10^10 K or 1 MeV, neutrinos could travel across the then-observable Universe with little chance of interacting, something called "decoupling" ( Chronology of the universe). These neutrinos' momentum-distribution temperature is now 1.9 K, colder than the CMB.

Returning to recombination, the Universe's composition was something like
[TABLE="class: grid"]
[TR]
[TD]Dark Matter[/TD]
[TD]0.63[/TD]
[/TR]
[TR]
[TD]Photons[/TD]
[TD]0.15[/TD]
[/TR]
[TR]
[TD]Baryonic Matter[/TD]
[TD]0.12[/TD]
[/TR]
[TR]
[TD]Neutrinos[/TD]
[TD]0.10[/TD]
[/TR]
[/TABLE]
Around the time of nucleosynthesis, the mix was
[TABLE="class: grid"]
[TR]
[TD]Photons[/TD]
[TD]0.59[/TD]
[/TR]
[TR]
[TD]Neutrinos[/TD]
[TD]0.41[/TD]
[/TR]
[/TABLE]
Even earlier, at a little before decoupling,
[TABLE="class: grid"]
[TR]
[TD]Neutrinos[/TD]
[TD]0.49[/TD]
[/TR]
[TR]
[TD]Electrons[/TD]
[TD]0.33[/TD]
[/TR]
[TR]
[TD]Photons[/TD]
[TD]0.19[/TD]
[/TR]
[/TABLE]
where electrons include positrons. Each kind of particle contributes
(# spin states) * (# charge states) * (# flavors) * (statistics factor: bosons 1, fermions 7/8)

 

[repoman]

https://en.wikipedia.org/wiki/Neutrino_decoupling

So for the first reaction, it must be mediated with a W or Z boson, right?

The reason that relic neutrinos are hard to detect is because the W and Z bosons are so massive and all that entails, right?

 

[lpetrich]

That's essentially it. That is also why the weak interaction is named that.

Neutrinos' interaction cross section goes roughly as (interaction energy)^2, so that's why neutrino decoupling happened, and that's why the cosmic neutrino background will be very difficult to detect directly.

 

[repoman]

Do extremely high velocity particles (cosmic rays or in accelerators) blueshift these relic neutrinos and interact with them to any measurable degree?

sort of like this:

https://en.wikipedia.org/wiki/Greisen%E2%80%93Zatsepin%E2%80%93Kuzmin_limit

The Greisen–Zatsepin–Kuzmin limit (GZK limit) is a theoretical upper limit on the energy of cosmic ray protons traveling from other galaxies through the intergalactic medium to our galaxy. The limit is 5×10^19 eV, or about 8 joules. The limit is set by slowing-interactions of the protons with the microwave background radiation over long distances (~160 million light-years). The limit is at the same order of magnitude as the upper limit for energy at which cosmic rays have experimentally been detected. For example, one extreme-energy cosmic ray has been detected which appeared to possess a record 3.12×10^20 eV (50 joules) of energy (about the same as the kinetic energy of a 95 km/h baseball).

So, take an 8 joule proton as the extreme case. What would a head on relic neutrino look like to it? It would still be a low-ish energy neutrino, right? I am not sure how to do the math.

Found this old article:

Cosmic Ray Neutrino Annihilation on Relic Neutrinos Revisited: A Mechanism for Generating Air Showers above the Greisen-Zatsepin-Kuzmin Cut-off

https://arxiv.org/abs/hep-ph/9710431

 

[lpetrich]

That's the  Greisen–Zatsepin–Kuzmin limit:

(CMB photon) + (proton) -> (delta baryon) -> (nucleon) + (pion)

Nucleon = proton and neutron

A neutrino could also do this, with a virtual W or Z striking the proton. Delta baryons have a mass of around 1232 MeV, around 294 MeV more than the rest-mass energy of a proton. This means that in the center-of-mass frame, where the total 3-momentum is zero, the photon must have an energy of 259 MeV, making it a very energetic gamma ray.

A neutrino causing that reaction must have at least that energy, and the reaction rate is roughly ((energy)/(100 GeV))^4 relative to a comparable electromagnetic reaction rate. That factor is about 10^(-10).

So a high-energy cosmic-ray proton won't interact with cosmic-background neutrinos nearly as much as with cosmic-backgound photons.