Could the momentum of light explain the effect known as "dark energy"? I know the distances between galaxies are wast, but so are the surface areas of galaxies, as well as all the stars emitting the light. Would be interesting to see a calculation of the fate of the universe if this was true, perhaps gravity would pull everything together again after the stars burnt out, and we'd have a cycle of big bangs. Any thoughts?
No. Energy and momentum of light in the universe are well-known (because we can see it) and they are a small positive (=attractive) contribution to the total energy-density. Please note that we don't allow wild speculations beyond actual physics here.
Most of the light energy in the universe is actually contained within the CMBR, and not from the light radiated by the stars! Even then, the CMBR accounts for only a tiny fraction of the total energy density of the universe today. Also, as mfb stated, this effect is well accounted for and would produce a deceleration in the expansion of the universe, not an acceleration.
[itex][/itex]the energy-density today can be calculated. Here is one method of estimating the energy-density today, though the paper calculates the energy density of photons as well as radiation http://astro.dur.ac.uk/~csf/level1/Cosmich/lecture_7-8_notes.pdf this paper has roughly the same energy-density for photons. [tex]\Omega_\gamma\approx5*10^{-5}[/tex] variations occur in rounding, method used etc. http://iopscience.iop.org/1742-6596/354/1/012009/pdf/1742-6596_354_1_012009.pdf I've read numerous textbooks, articles etc that all have variations in the energy-density, though they are all close the the value I posted
Mordred provided them. :) His number is the one I'm familiar with. If you wanted actual numbers with actual units, using ##\rho_{crit}\approx\rho_0=9\times 10^{-10}J/m^3## we get ##\rho_\gamma\approx 5\times 10^{-14}J/m^3##
From the cosmic energy inventory: 10^{-4.3} or 5*10^{-5} for CMB 10^{-5.8} or 1.5*10^{-6} for "optical" light, and just a bit more for non-CMB light in general Those numbers are relative to the critical density, where dark matter has ~.23 and dark energy ~.72.