Will electrons, and other particles, also loose energy as they travel through the cosmos? They have wavelengths. Do they get "stretched"? My guess is that the EM force, somehow, counteracts this effect. What about neutrinos?
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2$\begingroup$ Are you asking if the de Broglie wavelength of matter will red-shift and effectively make the matter lose mass or momentum? $\endgroup$– JimCommented Aug 30, 2014 at 19:28
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$\begingroup$ So I never considered this. I don't see why it wouldn't stretch the de Broglie wavelength, which would decrease the object's peculiar velocity. I looked around but I didn't see any mention of that sort of effect. Perhaps someone knows off-hand if that is an effect. It could be an interesting idea to explore. I doubt there would be much in the way of observational evidence. But it could be good for a fun weekend or something. $\endgroup$– JimCommented Aug 30, 2014 at 20:29
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$\begingroup$ You don't have to appeal to quantum mechanics for this. This is a purely classical fact about general relativity. Cosmologists generally talk about cosmological models as having a component of "dust," i.e., nonrelativistic matter, where a dust particle is some object such as a galaxy or cluster of galaxies. During cosmological expansion, the velocities of dust particles relative to the Hubble flow have systematically decreased. This is a good thing for us -- otherwise we'd live among galaxies colliding at relativistic speeds. You can calculate the de Broglie wavelength of a galaxy if you like. $\endgroup$– user4552Commented Aug 31, 2014 at 23:55
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The answer is yes. The de Broglie wavelengths of freely propagating particles (i.e. forget the influence of interactions and gravity perturbations, just consider the Universe as a whole) are redshifted by the expansion of the universe. Another way of saying this is that their peculiar momenta with respect to a co-moving local volume decrease as the inverse of the scale factor.
Neutrinos are an example of a particle with a non-zero mass (maybe of order 0.1 eV - see http://adsabs.harvard.edu/abs/2014PhRvL.112e1303B ). They decouple from the rest of the Universe at about 1 second and freely propagate. The expansion then reduces their momenta to the extent that they should have a temperatures $<2$K in the present-day Universe, typical kinetic energies of 0.2 meV (e.g. see http://adsabs.harvard.edu/abs/2010PhRvD..82f2001K ) and may have speeds of only (depending on their actual masses) perhaps $\sim 10^3-10^4$ km/s and so are non-relativistic.
Electrons would behave in the same way, if they could be considered not to be strongly (or rather electromagnetically!) interacting with other particles and photons. I don't think this can be satisfied except in the very early universe and a typical free, intergalactic electron in the present day universe has an energy of $\sim 0.1$ keV due to heating by radiation from stars and galaxies.
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1$\begingroup$ @user12262 Freely propagating in exactly the same sense as a CMB photon is freely propagating and has a decreasing momentum; subject only to the expansion of the universe and not other interactions. $\endgroup$– ProfRobCommented Aug 31, 2014 at 11:21
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1$\begingroup$ Found a good explanation also here: books.google.com/… $\endgroup$– yalisCommented Aug 31, 2014 at 18:32
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1$\begingroup$ @user12262 The idea of a non-interacting particle seems quite straightforward to me. It has a simple wavefunction, and a wavelength and this wavelength is increased by the expansion of the universe. Perhaps I just don't see the subtleties. Jim Decoupling takes place at about $kT=2$ MeV so the lost momentum is about 2 MeV/c. Why would the average speed by anisotropic? $\endgroup$– ProfRobCommented Aug 31, 2014 at 22:42
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1$\begingroup$ @Jim I'm not cosmologically informed to argue much about isotropy. I see no reason why initially the C$\nu$B shouldn't be as isotropic as the CMB. As the $\nu$ become non-rel. they will become anisotropic as they fall into potential wells. This affects structure formation and offers a route to determining neutrino masses. Two more excellent presentations and a paper I have been looking at are www-physics.lbl.gov/seminars/old/Petr_Vogel.pdf and darkuniverse.uni-hd.de/pub/Main/WinterSchool08Slides/… and adsabs.harvard.edu/abs/2014PhRvL.112e1303B $\endgroup$– ProfRobCommented Sep 1, 2014 at 16:14
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1$\begingroup$ @RobJeffries: Oops, sorry, I was wrong about the cosmic neutrino background. Undid the -1. $\endgroup$– user4552Commented Sep 1, 2014 at 16:48