I understand that primordial neutrinos (having been emitted with some small rest mass) are thought to have lost much of their originall energy and are considered by some to be potential dark matter candidates. Please see http://en.wikipedia.org/wiki/Cosmic_neutrino_background http://kicp.uchicago.edu/research/highlights/highlight_2009-11-19.html http://arxiv.org/abs/hep-ph/0602058 http://wwwth.mpp.mpg.de/members/raffelt/mypapers/200810.pdf and http://indico.cern.ch/event/223704/session/23/contribution/16/material/slides/0.pdf.

Neutrinos obey nature's speed limit, according to new results from an Italian experiment. The finding, posted to the preprint server arXiv.org, contradicts a rival claim that neutrinos could travel faster than the speed of light.

Neutrinos are tiny, electrically neutral particles produced in nuclear reactions. Last September, an experiment called OPERA turned up evidence that neutrinos travel faster than the speed of light (see 'Particles break light speed limit'). Located beneath the Gran Sasso mountain in central Italy, OPERA detected neutrinos sent from CERN, Europe's premier particle-physics laboratory near Geneva, Switzerland. According to the group's findings, neutrinos made the 731-kilometre journey 60 nanoseconds faster than predicted if they had travelled at light speed.

The announcement made international headlines, but physicists were deeply sceptical. The axiom that nothing travels faster than light was first formulated by Albert Einstein and is a cornerstone of modern physics. OPERA defended its announcement, saying that it could find no flaw in its measurement.

Now another experiment located just a few metres from OPERA has clocked neutrinos travelling at roughly the speed of light, and no faster. Known as ICARUS, the rival monitored a beam of neutrinos sent from CERN in late October and early November of last year. The neutrinos were packed into pulses just 3 nanoseconds long. That meant that the timing could be measured far more accurately than the original OPERA measurement, which used 10-microsecond pulses.

“Our results are in agreement with what Einstein would like to have,” says Carlo Rubbia, the spokesperson for ICARUS and a Nobel prizewinning physicist at CERN. Neutrinos measured by the experiment arrived within just 4 nanoseconds of the time that light travelling through a vacuum would take to cover the distance, well within the experimental margin of error.

The universe is a very difficult thing to visualise, but it is not correct to assume that all the neutrinos emitted at the big bang are now at the boundary travelling outwards. It is true that they travel at almost the speed of light and almost never interact with other matter. However, since we are inside the universe, we are inside the volume from which the neutrinos were emitted (although that volume has increased enormously since then). It is analogous to the cosmic microwave background, which is made up of light that was emitted soon after the big bang, and since then has been travelling at the speed of light through the universe. We see that now as a uniform background of photons coming from all directions, because we see light that was emitted isotropically from all parts of the universe all around us. 

Due to their positive mass, as deduced from the oscillation that neutrinos present, each neutrino is actually a superposition of at least three mass states with mass ranging from 0.01 up to 0.2 eV/c^2, less than 2 millionths of an electron mass.  Yet with this tiny mass the neutrinos created 1 sec after the Big Bang must travel at a speed of only about  1000 km/s today,  300 times slower than light, which means that the cosmological neutrinos we could detect with future instruments would have come from only a few Mpc (megaparsec) from us, instead of Gpc for photons.    

Neutrinos should not be seen as localized concentration of mass, but rather as quantum waves that spread over Mpc distances.  They behave as localized mass/energy concentration only when detected. 

Thanks Daniel, but can you explain why "the neutrinos created 1 sec after the Big Bang must travel at a speed of only about 1000 km/s today, 300 times slower than light"?

In simple terms photons or other particles exchange energy and momentum with the rest of the expanding Universe through gravitational interaction.  According to special relativity photons cannot slow down as they have zero mass, they can only lower their frequency, in proportion to the Universe scale.  Particles with positive mass cannot lower their rest mass energy mc2 but only their kinetic energy. Particle physicists accelerate everyday particles from zero to almost the speed of light and verify that special relativity works very well.   For each kind of particle with positive mass there is a Universe scale  at which their kinetic energy is comparable to their rest mass energy.  For neutrinos  this happens around a scale that was a few 1'000 times smaller than now (the exact scale is uncertain due to the uncertainties about neutrino masses).  Before that the neutrinos were moving  almost at the speed of light, and after that their speeds have decreased more and more inversely to the scale. 

Thank you Daniel, I beleive you are right as I'm not an expert in this field. But for gravity to reduce the speed of a particle moving in straight line, I think this implies that there should be some inhomogeneity in the gravity field, otherwise all the forces would cancel and there would not be any deceleration. Is this correct?

The point is that we have a time-dependent, expanding mass.  This would also work with a finite homogeneous exploding sphere in Newtonian gravity,  the expansion speed would automatically decrease to compensate the decreasing potential energy.

In Einsteinian gravity it is a bit harder to imagine the expansion of space-time, but the solutions of Einstein equations coincide with Newton gravity in the limit of weak gravity and asymptotic flat space.

Fabrice, neutrinos were copiously produced during big bang nucleosynthesis and we now know that these particles have a small but non-zero mass, something like 0.05eV. As the universe expanded, the neutrinos steadily coooled down. This cooling did not follow exactly the same progression as the reduction in temperature of the cosmic microwave background (initially 3000K, now 2.7K). The relic neutrino background formed much earlier than the CMB and is now much cooler than it. When a photon "cools down" its frequency reduces but its speed does not. However, since neutrinos have mass, they necessarily move with subluminal velocities. The typical speed (in km/s) of a relic neutrino at redshift z is given by the formula 161(1+z)/m where m is the neutrino mass. Assuming m~0.05eV this gives abut 3000 km/s (just 1% the speed of light and so distinctly nonrelativistic). However, this is still too fast for their capture by any of the gravitationally bound structures of the universe at the present time (though that will change in the future). Just as the photons of the CMB stream towards us from all directions, these relic neutrinos pervade the space we inhabit (there are several hundred per cubic cm). The neutrinos are not all near the boundary of the universe for the same reasons that the CMB photons are not. Besides, there may be no boundary. Although relic neutrinos are rivalled in abundance only by CMB photons, we have yet to detect a single example. This is staggering when we consider that there may be as many as 10^15 of these particles passing through our bodies each second!

Robin has already given the main answers.

Let me just add that relic neutrinos that are everywhere around us have now an average kinetic energy of about 0.25 meV, which is much smaller than their mass energy, which is some 50-100 meV. Consequently they do not move any more at speeds comparable with light, in the frame of the big bang. They are non relativistic. We move amongst them with our Galaxy at several hundred kilometers per second

When the universe was very dense and hot neutrinos did interact with the other types of matter. When temperature and density became sufficiently smaller neutrinos did not do that anymore. Notice however that when the cosmic neutrino background and later the CMB formed neutrinos were still relativistic, namely their kinetic energy was much larger than their rest energy, they were still "hot". This is why they do not contribute appreciably to dark matter, which is "cold".

As for the claim by the OPERA experiment of faster than light neutrinos, no other experiment at Gran Sasso confirmed the claim. OPERA itself found out were they had done the mistake

While it's been stated otherwise, as I understand warm and mixed dark matter scenarios have not been definitively discarded: cold dark matter suffers certain limitations in explaining the number of galaxy clusters and ‘cored’ dark matter halos.

See http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.112.161303 and http://arxiv.org/abs/1403.0954 for example. Also see http://arxiv.org/abs/1306.2314.

The Universe becomes transparent to neutrinos at a very early time (about 1 Second) - the number density of these neutrinos is 3/4 (or maybe 2/3 - can't remember) the number density of the microwave background photons.  There are 400 MWB photons per cc and hence order 300 neutrinoes per cubic centimenter.   These, by far dominate the neutrino count in the Universe.

G. Bothun,

"These, by far dominate the neutrino count in the Universe."

Did you mean to say that neutrinos by far dominate the particle count in the Universe?

No, cosmological neutrinos dominate the neutrino count

there are still more photons in the universe than neutrinoes

Less than 1 second after Big Bang all particles were mixed in a very dense hot “soap” and interacted. During 1-2 s after Big Bang the space expanded so much that the matter cooled enough and neutrinos stopped to interact with particles. From that time they fly freely in all directions. What do we see now? Relic neutrinos continue flying in all directions and the Universe continues to expand. The number of relic neutrinos is constant. Due to space expansion their density decreased to =~ 300 neutrinos/cm^3, and the energy decreased to =~ 1.9K (K is a unit of energy; for comparison: at the first second after Big Bang it was 10^10 K). Thus the space is expanding with the matter that is inside, and relic neutrinos fill the space more or less uniformly with decreasing density and energy. They does not concentrate near the boundary of the Universe.

This is similar to relic radiation. Relic photons began to fly across the space in all directions (when the Universe was 379,000 years old) with the energy of visible light. Now their energy is in the radio-frequency band (it decreased to T =~ 2.7K). Their density also decreases, now it is =~ 400 photons/cm^3.

CMB photons are thought to have been emitted at infrared frequencies by the hot, dense matter of the recombination epoch, when density was suddenly diminished by the binding of free electrons to protons to form neutral hydrogen atoms. The CMB photons that we detect arrive from all directions but, having no rest mass, they have all been effectively linearly propagating at the speed of light for more than 13 billion years.

As I understand, observations of neutrino oscillations indicate that they have some small rest mass – making relic neutrinos no longer relativistic. As a result, unlike photons they may become gravitationally bound within large scale structures…

While the characteristics of at least identifiable CMB photons can be confirmed by observation, relic neutrinos may never be detected in quantities sufficient to confirm their actual properties.

James

the CMB photons have been, rather than can be, detected and are being observed with increasing sensitivity and precision.

relic neutrinos are extremely difficult to detect, but several groups are developing techniques aiming at that in a future. Foreseeing now that these efforts will never succeed in any future is deprived of any scientific basis

Alessandro,

I stated not that CMB photons can be detected, but that “… characteristics of at least identifiable CMB photons can be confirmed by observation…” Obviously they have been detected for many decades now…

I did not doom all efforts to detect relic neutrinos to failure – my statement was qualified: “… relic neutrinos may never be detected in quantities sufficient to confirm their actual properties.”

I hope that relic neutrinos can someday be detected in sufficient quantities to confirm (or deny) their hypothesized characteristics.

Best wishes to all such efforts!

Cosmologists keep saying the neutrino background has temperature T=1.9K while actually they want to say that their energy corresponds to kT, with k Boltzmann's constant.  This habit comes from the time neutrinos were commonly assumed to be massless.  In that case, like for photons, energy can be assimilated to a temperature because if they would thermalize with a thermometer a temperature T would be measured.

But since neutrinos are massive, nowadays a substantial part of their energy is in their rest mass c^2.  A thermometer only measures the random kinetic energy part.  The  temperature that would be measured  if a huge thermometer would be brought to thermal equilibrium with the the neutrino background would be rather in the 0.001K range (depending on their still uncertain actual mass).