For a wavelength of the size of the universe, do virtual and real photons differ? Some theories of quantum gravity assume that very low temperatures of 10^-30 K arise - roughly corresponding to the temperature of a black hole with the size of the universe. 
Such a low temperature would yield photons whose wavelength is roughly the size of the universe. Is it possible to distinguish, for such "huge" (i.e., large-wavelength) photons, real from virtual photons?
A related question: can such "huge", i.e., cosmic-wavelength photons be real (i.e. on-shell) at all? Or are such huge photons always virtual (i.e. off-shell)? One could argue that for such cosmic-wavelength photons, the uncertainty relation does not allow to achieve on-shell state. 
 A: 
Such a low temperature would yield photons whose wavelength is roughly the size of the universe. Is it possible to distinguish, for such huge photons, real from virtual photons?

Lets clear up the terms.
Take a real photon. What does the wave length represent?  It comes from taking the $E=hν$ and assuming the frequency to be the frequency of the imaginary number $Ψ$ wavefunction whose  $Ψ^*Ψ$ ,  is equal to the probability to find a photon at an (x,y,z) as the photon footprints seen in this single photon at a time experiment, see image..
So for a real photon such a large wavelength means that the probability to find it at an (x,y,z) is very very small. I cannot imagine the experiment and how long it should wait to get a single hit ( it will of course depend on the flux etc).
What is a virtual photon?
A virtual photon is not measurable as it is the exchange of photon number quantum numbers under an integral, it is off mass shell and only the integration over virtual photons indicates their existence.

Thus there is no meaning in comparing virtual photons of very large wavelength, they may always exist under an integral, and a real photon of energy $E=hν$ . Virtual ones are mathematical constructs , while real ones carry energy and momentum in a four vector, and have invariant mass zero.
The real photons are not huge, as I explained above, they are always point particles . It is just that their energy is so small that the probability of finding one is practically zero.
